Mathematische Nachrichten最新文献

{"title":"Extrapolation to mixed Herz spaces and its applications","authors":"Mingquan Wei","doi":"10.1002/mana.202100134","DOIUrl":"10.1002/mana.202100134","url":null,"abstract":"<p>In this paper, we extend the extrapolation theory to mixed Herz spaces <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mover>\u0000 <mi>K</mi>\u0000 <mo>̇</mo>\u0000 </mover>\u0000 <mover>\u0000 <mi>q</mi>\u0000 <mo>⃗</mo>\u0000 </mover>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>,</mo>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msubsup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$dot{K}^{alpha,p}_{vec{q}}(mathbb {R}^n)$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>K</mi>\u0000 <mover>\u0000 <mi>q</mi>\u0000 <mo>⃗</mo>\u0000 </mover>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>,</mo>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msubsup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$K^{alpha,p}_{vec{q}}(mathbb {R}^n)$</annotation>\u0000 </semantics></math>. To prove the main result, we first study the dual spaces of mixed Herz spaces, and then give the boundedness of the Hardy–Littlewood maximal operator on mixed Herz spaces. By using the extrapolation theorems, we obtain the boundedness of many integral operators on mixed Herz spaces. We also give a new characterization of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mi>bounded</mi>\u0000 <mspace></mspace>\u0000 <mi>mean</mi>\u0000 <mspace></mspace>\u0000 <mi>oscillation</mi>\u0000 <mspace></mspace>\u0000 <mi>space</mi>\u0000 </mrow>\u0000 <mspace></mspace>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>BMO</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annot","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140034771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Totally geodesic Lagrangian submanifolds of the pseudo-nearly Kähler \u0000 \u0000 \u0000 SL\u0000 (\u0000 2\u0000 ,\u0000 R\u0000 )\u0000 ×\u0000 SL\u0000 (\u0000 2\u0000 ,\u0000 R\u0000 )\u0000 \u0000 $mathrm{SL}(2,mathbb {R})times mathrm{SL}(2,mathbb {R})$","authors":"Mateo Anarella,&nbsp;J. Van der Veken","doi":"10.1002/mana.202300351","DOIUrl":"10.1002/mana.202300351","url":null,"abstract":"<p>In this paper, we study Lagrangian submanifolds of the pseudo-nearly Kähler <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>SL</mi>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 <mo>×</mo>\u0000 <mi>SL</mi>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{SL}(2,mathbb {R})times mathrm{SL}(2,mathbb {R})$</annotation>\u0000 </semantics></math>. First, we show that they split into four different classes depending on their behavior with respect to a certain almost product structure on the ambient space. Then, we give a complete classification of totally geodesic Lagrangian submanifolds of this space.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140034744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the zero set of the holomorphic sectional curvature","authors":"Yongchang Chen,&nbsp;Gordon Heier","doi":"10.1002/mana.202300424","DOIUrl":"10.1002/mana.202300424","url":null,"abstract":"<p>A notable example due to Heier, Lu, Wong, and Zheng shows that there exist compact complex Kähler manifolds with ample canonical line bundle such that the holomorphic sectional curvature is negative semi-definite and vanishes along high-dimensional linear subspaces in every tangent space. The main result of this note is an upper bound for the dimensions of these subspaces. Due to the holomorphic sectional curvature being a real-valued bihomogeneous polynomial of bidegree (2,2) on every tangent space, the proof is based on making a connection with the work of D'Angelo on complex subvarieties of real algebraic varieties and the decomposition of polynomials into differences of squares. Our bound involves an invariant that we call the holomorphic sectional curvature square decomposition length, and our arguments work as long as the holomorphic sectional curvature is semi-definite, be it negative or positive.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140007966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Extension and embedding theorems for Campanato spaces on \u0000 \u0000 \u0000 C\u0000 \u0000 0\u0000 ,\u0000 γ\u0000 \u0000 \u0000 $C^{0,gamma }$\u0000 domains","authors":"Damiano Greco,&nbsp;Pier Domenico Lamberti","doi":"10.1002/mana.202300092","DOIUrl":"10.1002/mana.202300092","url":null,"abstract":"<p>We consider Campanato spaces with exponents <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mo>,</mo>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 <annotation>$lambda, p$</annotation>\u0000 </semantics></math> on domains of class <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>γ</mi>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$C^{0,gamma }$</annotation>\u0000 </semantics></math> in the <i>N</i>-dimensional Euclidean space endowed with a natural anisotropic metric depending on <span></span><math>\u0000 <semantics>\u0000 <mi>γ</mi>\u0000 <annotation>$gamma$</annotation>\u0000 </semantics></math>. We discuss several results including the appropriate Campanato's embedding theorem and we prove that functions of those spaces can be extended to the whole of the Euclidean space without deterioration of the exponents <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mo>,</mo>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 <annotation>$lambda, p$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140007976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Energy behavior for Sobolev solutions to viscoelastic damped wave models with time-dependent oscillating coefficient","authors":"Xiaojun Lu","doi":"10.1002/mana.202200431","DOIUrl":"10.1002/mana.202200431","url":null,"abstract":"<p>In this work, we study the asymptotic behavior of the structurally damped wave equations arising from the viscoelastic mechanics. We are particularly interested in the complicated interaction of the time-dependent oscillating coefficients on the Dirichlet Laplacian operator and the structurally damped terms. On the one hand, by the application of WKB analysis, we explore the asymptotic energy estimates of the wave equations influenced by four types of oscillating mechanisms. On the other hand, in order to prove the optimality of the energy estimates for the critical cases, typical coefficients and initial Cauchy data will be constructed to show the lower bound of the energy growth rate by the application of instability arguments.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140007840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Metivier inequality and ultradifferentiable hypoellipticity","authors":"Paulo D. Cordaro,&nbsp;Stefan Fürdös","doi":"10.1002/mana.202300147","DOIUrl":"10.1002/mana.202300147","url":null,"abstract":"<p>In 1980, Métivier characterized the analytic (and Gevrey) hypoellipticity of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$L^2$</annotation>\u0000 </semantics></math>-solvable partial linear differential operators by a priori estimates. In this note, we extend this characterization to ultradifferentiable hypoellipticity with respect to Denjoy–Carleman classes given by suitable weight sequences. We also discuss the case when the solutions can be taken as hyperfunctions and present some applications.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300147","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140007851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A singular growth phenomenon in a Keller–Segel–type parabolic system involving density-suppressed motilities","authors":"Yulan Wang,&nbsp;Michael Winkler","doi":"10.1002/mana.202300361","DOIUrl":"10.1002/mana.202300361","url":null,"abstract":"<p>A no-flux initial-boundary value problem for\u0000\u0000 </p><p>Under the assumption that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>&gt;</mo>\u0000 <mfrac>\u0000 <mi>n</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mfrac>\u0000 </mrow>\u0000 <annotation>$alpha &amp;gt;frac{n}{n-2}$</annotation>\u0000 </semantics></math>, it is shown that for each <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$m&amp;gt;0$</annotation>\u0000 </semantics></math>, there exist <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$T&amp;gt;0$</annotation>\u0000 </semantics></math> and a positive <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>v</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mi>W</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$v_0in W^{1,infty }(Omega)$</annotation>\u0000 </semantics></math> with the property that whenever <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>u</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mi>W</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$u_0in W^{1,infty }(Omega)$</annotation>\u0000 </semantics></math> is nonnegative with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300361","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139956188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"I-surfaces from surfaces with one exceptional unimodal point","authors":"Sönke Rollenske,&nbsp;Diana Torres","doi":"10.1002/mana.202300218","DOIUrl":"10.1002/mana.202300218","url":null,"abstract":"<p>We complement recent work of Gallardo, Pearlstein, Schaffler, and Zhang, showing that the stable surfaces with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>K</mi>\u0000 <mi>X</mi>\u0000 <mn>2</mn>\u0000 </msubsup>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$K_X^2 =1$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>χ</mi>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>O</mi>\u0000 <mi>X</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$chi (mathcal {O}_X) = 3$</annotation>\u0000 </semantics></math> they construct are indeed the only ones arising from imposing an exceptional unimodal double point.</p><p>In addition, we explicitly describe the birational type of the surfaces constructed from singularities of type <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mn>12</mn>\u0000 </msub>\u0000 <annotation>$E_{12}$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mn>13</mn>\u0000 </msub>\u0000 <annotation>$E_{13}$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>E</mi>\u0000 <mn>14</mn>\u0000 </msub>\u0000 <annotation>$E_{14}$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300218","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139955953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Density of smooth functions in Musielak–Orlicz–Sobolev spaces \u0000 \u0000 \u0000 \u0000 W\u0000 \u0000 k\u0000 ,\u0000 Φ\u0000 \u0000 \u0000 \u0000 (\u0000 Ω\u0000 )\u0000 \u0000 \u0000 $W^{k,Phi }(Omega)$","authors":"Anna Kamińska,&nbsp;Mariusz Żyluk","doi":"10.1002/mana.202300232","DOIUrl":"10.1002/mana.202300232","url":null,"abstract":"<p>We consider here Musielak–Orlicz–Sobolev (MOS) spaces <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>W</mi>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>,</mo>\u0000 <mi>Φ</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$W^{k,Phi }(Omega)$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mi>Ω</mi>\u0000 <annotation>$Omega$</annotation>\u0000 </semantics></math> is an open subset of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^d$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>∈</mo>\u0000 <mi>N</mi>\u0000 <mo>,</mo>\u0000 </mrow>\u0000 <annotation>$kin mathbb {N,}$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mi>Φ</mi>\u0000 <annotation>$Phi$</annotation>\u0000 </semantics></math> is a Musielak–Orlicz function. The main outcomes consist of the results on density of the space of compactly supported smooth functions <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>C</mi>\u0000 <mi>C</mi>\u0000 <mi>∞</mi>\u0000 </msubsup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$C_C^infty (Omega)$</annotation>\u0000 </semantics></math> in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>W</mi>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>,</mo>\u0000 <mi>Φ</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$W^{k,Phi }(Omega)$</annotation>\u0000 </semantics></math>. One section is devoted to compare the various conditions on <span></span><math>\u0000 <semantics>\u0000 <mi>Φ</mi>\u0000 <annotation>$Phi$</annotation>\u0000 </semantics></math> appearing in the literature in the context of maximal operator and density theorems in MOS spaces. The assum","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139955952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Mullins–Sekerka problem via the method of potentials","authors":"Joachim Escher,&nbsp;Anca-Voichita Matioc,&nbsp;Bogdan-Vasile Matioc","doi":"10.1002/mana.202300350","DOIUrl":"10.1002/mana.202300350","url":null,"abstract":"<p>It is shown that the two-dimensional Mullins–Sekerka problem is well-posed in all subcritical Sobolev spaces <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mi>r</mi>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$H^r({mathbb {R}})$</annotation>\u0000 </semantics></math> with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>3</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$rin (3/2,2)$</annotation>\u0000 </semantics></math>. This is the first result, where this issue is established in an unbounded geometry. The novelty of our approach is the use of the potential theory to formulate the model as an evolution problem with nonlinearities expressed by singular integral operators.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300350","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139956139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}