Annali di Matematica Pura ed Applicata最新文献

{"title":"On a sum of squares operator related to the Schrödinger equation with a magnetic field","authors":"Antonio Bove,&nbsp;Gregorio Chinni","doi":"10.1007/s10231-024-01434-2","DOIUrl":"10.1007/s10231-024-01434-2","url":null,"abstract":"<div><p>We study the analytic and Gevrey regularity for a “sum of squares” operator closely connected to the Schrödinger equation with minimal coupling. We however assume that the (magnetic) vector potential has some degree of homogeneity and that the Hörmander bracket condition is satisfied. It is shown that the local analytic/Gevrey regularity of the solution is related to the multiplicities of the zeroes of the Lie bracket of the vector fields.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140056109","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":"Remarks on the Levi core","authors":"Gian Maria Dall’Ara,&nbsp;Samuele Mongodi","doi":"10.1007/s10231-024-01432-4","DOIUrl":"10.1007/s10231-024-01432-4","url":null,"abstract":"<div><p>We investigate a few aspects of the notion of Levi core, recently introduced by the authors in Dall’Ara, Mongodi (J l’École Polytech Math 10:1047-1095, 2023): a basic finiteness question, the connection with Kohn’s algorithm, and with Catlin’s property (P).</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01432-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140074204","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":"Surfaces with Prym-canonical hyperplane sections","authors":"Martina Anelli","doi":"10.1007/s10231-024-01433-3","DOIUrl":"10.1007/s10231-024-01433-3","url":null,"abstract":"<div><p>In this paper, we will describe some general properties regarding surfaces with Prym-canonical hyperplane sections, determining also important conditions on the geometric genera of the possible singularities that such a surface can have. Moreover, we will construct new examples of this type of surfaces.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01433-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881514","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":"Some new asymptotic behaviors of a two-component b-family equations","authors":"Lijun Du,&nbsp;Xinglong Wu","doi":"10.1007/s10231-024-01429-z","DOIUrl":"10.1007/s10231-024-01429-z","url":null,"abstract":"<div><p>In this article, we investigate some new asymptotic behaviors of the solution for a two-component <i>b</i>-family equations. We first prove the persistence properties of the solution for Eq. (1.1) when the initial data decay logarithmically, algebraically at infinity with the power <span>(beta in (0,infty ))</span>. Subsequently, we obtain the infinite propagation of the solution to Eq. (1.1). If the initial data satisfy certain compact condition, then the nontrivial solution <i>u</i> of Eq. (1.1) immediately loses compactly supported. Meanwhile, the solution <i>u</i> decays exponentially as <span>(|x|rightarrow infty )</span>.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140082337","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":"Fractional Besov spaces and Hardy inequalities on bounded non-smooth domains","authors":"Jun Cao,&nbsp;Yongyang Jin,&nbsp;Zhuonan Yu,&nbsp;Qishun Zhang","doi":"10.1007/s10231-024-01430-6","DOIUrl":"10.1007/s10231-024-01430-6","url":null,"abstract":"<div><p>Let <span>(Omega )</span> be a bounded non-smooth domain in <span>(mathbb {R}^n)</span> that satisfies the measure density condition. In this paper, the authors study the interrelations of three basic types of Besov spaces <span>(B_{p,q}^s(Omega ))</span>, <span>(mathring{B}_{p,q}^s(Omega ))</span> and <span>(widetilde{B}_{p,q}^s(Omega ))</span> on <span>(Omega )</span>, which are defined, respectively, via the restriction, completion and supporting conditions with <span>(p,qin [1,infty ))</span> and <span>(sin (0,1))</span>. The authors prove that <span>(B_{p,q}^s(Omega )=mathring{B}_{p,q}^s(Omega )=widetilde{B}_{p,q}^s(Omega ))</span>, if <span>(Omega )</span> supports a fractional Besov–Hardy inequality, where the latter is proved under certain conditions on fractional Besov capacity or Aikawa’s dimension of the boundary of <span>(Omega )</span>.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140018534","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 density of “wild” initial data for the barotropic Euler system","authors":"Elisabetta Chiodaroli,&nbsp;Eduard Feireisl","doi":"10.1007/s10231-024-01423-5","DOIUrl":"10.1007/s10231-024-01423-5","url":null,"abstract":"<div><p>We show that the set of “wild data”, meaning the initial data for which the barotropic Euler system admits infinitely many <i>admissible entropy</i> solutions, is dense in the <span>(L^p)</span>-topology of the phase space.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01423-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140881322","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":"The Wolff hull of a compact holomorphic self-map on an infinite dimensional ball","authors":"M. Mackey,&nbsp;P. Mellon","doi":"10.1007/s10231-024-01427-1","DOIUrl":"10.1007/s10231-024-01427-1","url":null,"abstract":"<div><p>For large classes of (finite and) infinite dimensional complex Banach spaces <i>Z</i>, <i>B</i> its open unit ball and <span>(f:Brightarrow B)</span> a compact holomorphic fixed-point free map, we introduce and define the <i>Wolff hull</i>, <i>W</i>(<i>f</i>), of <i>f</i> in <span>(partial B)</span> and prove that <i>W</i>(<i>f</i>) is proximal to the images of all subsequential limits of the sequences of iterates <span>((f^n)_n)</span> of <i>f</i>. The Wolff hull generalises the concept of a Wolff point, where such a point can no longer be uniquely determined, and coincides with the Wolff point if <i>Z</i> is a Hilbert space. Recall that <span>((f^n)_n)</span> does not generally converge even in finite dimensions, compactness of <i>f</i> (i.e. <i>f</i>(<i>B</i>) is relatively compact) is necessary for convergence in the infinite dimensional Hilbert ball and all accumulation points <span>(Gamma (f))</span> of <span>((f^n)_n)</span> map <i>B</i> into <span>(partial B)</span> (for any topology finer than the topology of pointwise convergence on <i>B</i>). The target set of <i>f</i> is </p><div><div><span>$$begin{aligned} T(f)=bigcup _{g in Gamma (f)} g(B). end{aligned}$$</span></div></div><p>To locate <i>T</i>(<i>f</i>), we use a concept of closed convex holomorphic hull, <span>({text {Ch}}(x) subset partial B)</span> for each <span>(x in partial B)</span> and define a distinguished Wolff hull <i>W</i>(<i>f</i>). We show that the Wolff hull intersects all hulls from <i>T</i>(<i>f</i>), namely </p><div><div><span>$$begin{aligned} W(f) cap {text {Ch}}(x)ne emptyset hbox {for all} x in T(f). end{aligned}$$</span></div></div><p>If <i>B</i> is the Hilbert ball, <i>W</i>(<i>f</i>) is the Wolff point, and this is the usual Denjoy–Wolff result. Our results are for all reflexive Banach spaces having a homogeneous ball (or equivalently, for all finite rank <span>(JB^*)</span>-triples). These include many well-known operator spaces, for example, <i>L</i>(<i>H</i>, <i>K</i>), where either <i>H</i> or <i>K</i> is finite dimensional.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01427-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140437642","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":"(overline{Q}')-curvature flow on pseudo-Einstein CR manifolds","authors":"Ali Maalaoui,&nbsp;Vittorio Martino","doi":"10.1007/s10231-024-01425-3","DOIUrl":"10.1007/s10231-024-01425-3","url":null,"abstract":"<div><p>In this paper, we consider the problem of prescribing the <span>(overline{Q}')</span>-curvature on three-dimensional pseudo-Einstein CR manifolds. We study the gradient flow generated by the related functional, and we will prove its convergence to a limit function under suitable assumptions.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139960624","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 quasilinear Schrödinger equations on tori","authors":"Felice Iandoli","doi":"10.1007/s10231-024-01428-0","DOIUrl":"10.1007/s10231-024-01428-0","url":null,"abstract":"<div><p>We improve the result by Feola and Iandoli (J Math Pures Appl 157:243–281, 2022), showing that quasilinear Hamiltonian Schrödinger type equations are well posed on <span>(H^s({{mathbb {T}}}^d))</span> if <span>(s&gt;d/2+3)</span>. We exploit the sharp paradifferential calculus on <span>({{mathbb {T}}}^d)</span> developed by Berti et al. (J Dyn Differ Equ 33(3):1475–1513, 2021).</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01428-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139752909","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":"An abstract instability theorem of the bound states for Hamiltonian PDEs and its application","authors":"Jun Wang","doi":"10.1007/s10231-024-01426-2","DOIUrl":"10.1007/s10231-024-01426-2","url":null,"abstract":"<div><p>In this paper, the orbital instability theorem is introduced for Hamiltonian partial differential equation (PDE) systems. Our specific focus lies on the Schrödinger system featuring quadratic nonlinearity, and we apply the theorem to analyze its behavior. Our theorem establishes the abstract instability theorem for a specific class of Hamiltonian PDE systems. We consider the energy functional to be of class <span>(C^2)</span> rather than <span>(C^3)</span>, particularly when the second derivative of the energy exhibits multiple degenerate kernels. Using this theorem, we provide a comprehensive classification of the stability and instability of the semitrivial solution within the Hamiltonian PDE system featuring quadratic nonlinearity. This classification resolves an open problem previously posed by Colin et al. (Ann Inst Henri Poincaré Anal Non Linéaire 26:2211–2226, 2009), specifically in cases of homogeneous nonlinearity. Additionally, we present proof of instability results for synchronous solutions of Hamiltonian PDE systems. We believe that this abstract theorem constitutes a novel contribution with potential applicability in various situations beyond those specifically discussed in this paper.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139752710","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}