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Decay estimates for a class of wave equations on the Heisenberg group Heisenberg群上一类波动方程的衰变估计
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-04-20 DOI: 10.1007/s10231-023-01334-x
Manli Song, Jiale Yang
{"title":"Decay estimates for a class of wave equations on the Heisenberg group","authors":"Manli Song,&nbsp;Jiale Yang","doi":"10.1007/s10231-023-01334-x","DOIUrl":"10.1007/s10231-023-01334-x","url":null,"abstract":"<div><p>In this paper, we study a class of dispersive wave equations on the Heisenberg group <span>(H^n)</span>. Based on the group Fourier transform on <span>(H^n)</span>, the properties of the Laguerre functions and the stationary phase lemma, we establish the decay estimates for a class of dispersive semigroup on <span>(H^n)</span> given by <span>(e^{textrm{it}phi ({mathscr {L}})})</span>, where <span>(phi : {mathbb {R}}^+ rightarrow {mathbb {R}})</span> is smooth, and <span>({mathscr {L}})</span> is the sub-Laplacian on <span>(H^n)</span>. Finally, using the duality arguments, we apply the obtained results to derive the Strichartz inequalities for the solutions of some specific equations, such as the fractional Schrödinger equation, the fractional wave equation and the fourth-order Schrödinger equation.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50498448","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}
引用次数: 1
Uniform integrability in periodic homogenization of fully nonlinear elliptic equations 全非线性椭圆型方程周期均匀化中的一致可积性
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-04-15 DOI: 10.1007/s10231-023-01331-0
Sunghan Kim
{"title":"Uniform integrability in periodic homogenization of fully nonlinear elliptic equations","authors":"Sunghan Kim","doi":"10.1007/s10231-023-01331-0","DOIUrl":"10.1007/s10231-023-01331-0","url":null,"abstract":"<div><p>This paper is devoted to the study of uniform <span>(W^{1,frac{np}{n-p}})</span>- and <span>(W^{2,p})</span>-estimates for periodic homogenization problems of fully nonlinear elliptic equations. We establish sharp, global, large-scale estimates under the Dirichlet boundary conditions. The main novelty of this paper can be found in the characterization of the size of the “effective” Hessian and gradient of viscosity solutions to homogenization problems. Moreover, the large-scale estimates work in a large class of non-convex problems. It should be stressed that our global estimates are new even for the standard problems without homogenization.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01331-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50482552","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}
引用次数: 0
Bourgain, Brezis and Mironescu theorem for fractional Sobolev spaces with variable exponents 变指数分数阶Sobolev空间的Bourgain、Brezis和Mironescu定理
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-04-13 DOI: 10.1007/s10231-023-01333-y
Minhyun Kim
{"title":"Bourgain, Brezis and Mironescu theorem for fractional Sobolev spaces with variable exponents","authors":"Minhyun Kim","doi":"10.1007/s10231-023-01333-y","DOIUrl":"10.1007/s10231-023-01333-y","url":null,"abstract":"<div><p>A Bourgain–Brezis–Mironescu-type theorem for fractional Sobolev spaces with variable exponents is established for sufficiently regular functions. We prove, however, that a limiting embedding theorem for these spaces fails to hold in general.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50475788","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}
引用次数: 2
The varieties of bifocal Grassmann tensors 双焦点Grassmann张量的变种
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-04-07 DOI: 10.1007/s10231-023-01317-y
Marina Bertolini, Gilberto Bini, Cristina Turrini
{"title":"The varieties of bifocal Grassmann tensors","authors":"Marina Bertolini,&nbsp;Gilberto Bini,&nbsp;Cristina Turrini","doi":"10.1007/s10231-023-01317-y","DOIUrl":"10.1007/s10231-023-01317-y","url":null,"abstract":"<div><p>Grassmann tensors arise from classical problems of scene reconstruction in computer vision. In particular, bifocal Grassmann tensors, related to a pair of projections from a projective space onto view spaces of varying dimensions, generalize the classical notion of fundamental matrices. In this paper, we study in full generality the variety of bifocal Grassmann tensors focusing on its birational geometry. To carry out this analysis, every object of multi-view geometry is described both from an algebraic and geometric point of view, e.g., the duality between the view spaces, and the space of rays is explicitly described via polarity. Next, we deal with the moduli of bifocal Grassmann tensors, thus showing that this variety is both birational to a suitable homogeneous space and endowed with a dominant rational map to a Grassmannian.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01317-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50458110","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}
引用次数: 0
Non-solvable groups whose character degree graph has a cut-vertex. III 特征度图具有割顶点的不可解群。三、
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-04-06 DOI: 10.1007/s10231-023-01328-9
Silvio Dolfi, Emanuele Pacifici, Lucia Sanus
{"title":"Non-solvable groups whose character degree graph has a cut-vertex. III","authors":"Silvio Dolfi,&nbsp;Emanuele Pacifici,&nbsp;Lucia Sanus","doi":"10.1007/s10231-023-01328-9","DOIUrl":"10.1007/s10231-023-01328-9","url":null,"abstract":"<div><p>Let <i>G</i> be a finite group. Denoting by <span>(textrm{cd}(G))</span> the set of the degrees of the irreducible complex characters of <i>G</i>, we consider the <i>character degree graph</i> of <i>G</i>: this, is the (simple, undirected) graph whose vertices are the prime divisors of the numbers in <span>(textrm{cd}(G))</span>, and two distinct vertices <i>p</i>, <i>q</i> are adjacent if and only if <i>pq</i> divides some number in <span>(textrm{cd}(G))</span>. This paper completes the classification, started in Dolfi et al. (Non-solvable groups whose character degree graph has a cut-vertex. II, 2022. https://doi.org/10.1007/s10231-022-01299-3) and Dolfi et al. (Non-solvable groups whose character degree graph has a cut-vertex. I, 2022. https://doi.org/10.48550/arXiv.2207.10119), of the finite non-solvable groups whose character degree graph has a <i>cut-vertex</i>, i.e., a vertex whose removal increases the number of connected components of the graph. More specifically, it was proved in Dolfi et al. (Non-solvable groups whose character degree graph has a cut-vertex. I, 2022. https://doi.org/10.48550/arXiv.2207.10119 that these groups have a unique non-solvable composition factor <i>S</i>, and that <i>S</i> is isomorphic to a group belonging to a restricted list of non-abelian simple groups. In Dolfi et al. (Non-solvable groups whose character degree graph has a cut-vertex. II, 2022. https://doi.org/10.1007/s10231-022-01299-3) and Dolfi et al. (Non-solvable groups whose character degree graph has a cut-vertex. I, 2022. https://doi.org/10.48550/arXiv.2207.10119) all isomorphism types for <i>S</i> were treated, except the case <span>(Scong textrm{PSL}_{2}(2^a))</span> for some integer <span>(age 2)</span>; the remaining case is addressed in the present paper.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01328-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50455080","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}
引用次数: 1
Closure result for ( Gamma )-limits of functionals with linear growth 线性增长泛函的（Gamma）-极限的闭包结果
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-04-05 DOI: 10.1007/s10231-023-01322-1
Martin Jesenko
{"title":"Closure result for ( Gamma )-limits of functionals with linear growth","authors":"Martin Jesenko","doi":"10.1007/s10231-023-01322-1","DOIUrl":"10.1007/s10231-023-01322-1","url":null,"abstract":"<div><p>We consider integral functionals <span>( mathcal {F}^{(j)}_{varepsilon } )</span>, doubly indexed by <span>( varepsilon &gt; 0 )</span> and <span>(j in mathbb Ncup { infty })</span>, satisfying a standard linear growth condition. We investigate the question of <span>( Gamma )</span>-closure, i.e., when the <span>( Gamma )</span>-convergence of all families <span>( { mathcal {F}^{(j)}_{varepsilon } }_{varepsilon })</span> with finite <i>j</i> implies <span>( Gamma )</span>-convergence of <span>({ mathcal {F}^{(infty )}_{varepsilon } }_{varepsilon })</span>. This has already been explored for <i>p</i>-growth with <span>( p &gt; 1 )</span>. We show by an explicit counterexample that due to the differences between the spaces <span>( W^{1,1} )</span> and <span>( W^{1,p} )</span> with <span>( p &gt; 1 )</span>, an analog cannot hold. Moreover, we find a sufficient condition for a positive answer.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01322-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50450351","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}
引用次数: 0
On an elastic flow for parametrized curves in (mathbb {R}^{n}) suitable for numerical purposes 关于适用于数值目的的（mathbb｛R｝^｛n｝）中参数化曲线的弹性流
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-04-03 DOI: 10.1007/s10231-023-01329-8
Paola Pozzi
{"title":"On an elastic flow for parametrized curves in (mathbb {R}^{n}) suitable for numerical purposes","authors":"Paola Pozzi","doi":"10.1007/s10231-023-01329-8","DOIUrl":"10.1007/s10231-023-01329-8","url":null,"abstract":"<div><p>In Pozzi and Stinner (ESAIM: M2AN 57:445–466, 2023) a variant of the classical elastic flow for closed curves in <span>(mathbb {R}^{n})</span> was introduced, that is more suitable for numerical purposes. Here we investigate the long-time properties of such evolution demonstrating that the flow exists globally in time.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01329-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50443531","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}
引用次数: 1
Weighted symmetrization results for a problem with variable Robin parameter 变Robin参数问题的加权对称化结果
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-04-01 DOI: 10.1007/s10231-023-01313-2
Angelo Alvino, Francesco Chiacchio, Carlo Nitsch, Cristina Trombetti
{"title":"Weighted symmetrization results for a problem with variable Robin parameter","authors":"Angelo Alvino,&nbsp;Francesco Chiacchio,&nbsp;Carlo Nitsch,&nbsp;Cristina Trombetti","doi":"10.1007/s10231-023-01313-2","DOIUrl":"10.1007/s10231-023-01313-2","url":null,"abstract":"<div><p>By means of a suitable weighted rearrangement, we obtain various apriori bounds for the solutions to a Robin problem. Among other things, we derive a family of Faber-Krahn type inequalities.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01313-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50428280","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}
引用次数: 2
Positive flow-spines and contact 3-manifolds 正流脊和接触3歧管
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-03-30 DOI: 10.1007/s10231-023-01314-1
Ippei Ishii, Masaharu Ishikawa, Yuya Koda, Hironobu Naoe
{"title":"Positive flow-spines and contact 3-manifolds","authors":"Ippei Ishii,&nbsp;Masaharu Ishikawa,&nbsp;Yuya Koda,&nbsp;Hironobu Naoe","doi":"10.1007/s10231-023-01314-1","DOIUrl":"10.1007/s10231-023-01314-1","url":null,"abstract":"<div><p>A flow-spine of a 3-manifold is a spine admitting a flow that is transverse to the spine, where the flow in the complement of the spine is diffeomorphic to a constant flow in an open ball. We say that a contact structure on a closed, connected, oriented 3-manifold is supported by a flow-spine if it has a contact form whose Reeb flow is a flow of the flow-spine. It is known by Thurston and Winkelnkemper that any open book decomposition of a closed oriented 3-manifold supports a contact structure. In this paper, we introduce a notion of positivity for flow-spines and prove that any positive flow-spine of a closed, connected, oriented 3-manifold supports a contact structure uniquely up to isotopy. The positivity condition is critical to the existence of the unique, supported contact structure, which is also proved in the paper.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50526655","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}
引用次数: 3
Biconservative surfaces in the 4-dimensional Euclidean sphere 4维欧氏球面上的双保守曲面
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2023-03-28 DOI: 10.1007/s10231-023-01323-0
Simona Nistor, Cezar Oniciuc, Nurettin Cenk Turgay, Rüya Yeğin Şen
{"title":"Biconservative surfaces in the 4-dimensional Euclidean sphere","authors":"Simona Nistor,&nbsp;Cezar Oniciuc,&nbsp;Nurettin Cenk Turgay,&nbsp;Rüya Yeğin Şen","doi":"10.1007/s10231-023-01323-0","DOIUrl":"10.1007/s10231-023-01323-0","url":null,"abstract":"<div><p>In this paper, we study biconservative surfaces with parallel normalized mean curvature vector field (<i>PNMC</i>) in the 4-dimensional unit Euclidean sphere <span>(mathbb {S}^4)</span>. First, we study the existence and uniqueness of such surfaces. We obtain that there exists a 2-parameter family of non-isometric abstract surfaces that admit a (unique) <i>PNMC</i> biconservative immersion in <span>(mathbb {S}^4)</span>. Then, we obtain the local parametrization of these surfaces in the 5-dimensional Euclidean space <span>(mathbb {E}^5)</span>. We end the paper by proving that the substantial codimension of <i>PNMC</i> biconservative surfaces in <span>(mathbb {S}^n)</span>, <span>(nge 5)</span>, is equal to 2.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50521776","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}
引用次数: 0
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