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Annali di Matematica Pura ed Applicata最新文献

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A new Adams’ inequality involving the ( (frac{N}{2},p)-)Bilaplacian operators and applications to some biharmonic nonlocal equation 涉及( (frac{N}{2},p)-) Bilaplacian算子的一个新的Adams不等式及其在双调和非局部方程中的应用
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-09-23 DOI: 10.1007/s10231-024-01503-6
Sami Aouaoui
{"title":"A new Adams’ inequality involving the ( (frac{N}{2},p)-)Bilaplacian operators and applications to some biharmonic nonlocal equation","authors":"Sami Aouaoui","doi":"10.1007/s10231-024-01503-6","DOIUrl":"10.1007/s10231-024-01503-6","url":null,"abstract":"<div><p>In this paper, we prove some new inequality of Adams’ type for some new higher order Sobolev space whose norm is a combination of the norms of the <span>( frac{N}{2}-)</span>Bilaplacian and the <span>( p-)</span>Bilaplacian with <span>( p &lt; frac{N}{2} )</span> in the whole euclidean space <span>( mathbb {R}^N, N ge 4. )</span> The inequality proved is completely new. Next, an improvement of this inequality, inspired by the concentration-compactness principle of P. Lions, is also provided. This improvement is not trivial and its proof needs some new sophisticated tools. Finally, using this inequality, we treat in the last part of this work, some biharmonic elliptic quasilinear equation involving <span>( (frac{N}{2},p)-)</span>Bilaplacian operators and where the nonlinearities enjoy an exponential growth condition at infinity.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"733 - 757"},"PeriodicalIF":1.0,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688516","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
Stable solutions to fractional semilinear equations: uniqueness, classification, and approximation results 分数半线性方程的稳定解：唯一性、分类和近似结果
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-09-17 DOI: 10.1007/s10231-024-01497-1
Tomás Sanz-Perela
{"title":"Stable solutions to fractional semilinear equations: uniqueness, classification, and approximation results","authors":"Tomás Sanz-Perela","doi":"10.1007/s10231-024-01497-1","DOIUrl":"10.1007/s10231-024-01497-1","url":null,"abstract":"<div><p>We study stable solutions to fractional semilinear equations <span>((-Delta )^s u = f(u))</span> in <span>(Omega subset {mathbb {R}}^n)</span>, for convex nonlinearities <i>f</i>, and under the Dirichlet exterior condition <span>(u=g)</span> in <span>({mathbb {R}}^n {setminus } Omega)</span> with general <i>g</i>. We establish a uniqueness and a classification result, and we show that weak (energy) stable solutions can be approximated by a sequence of bounded (and hence regular) stable solutions to similar problems. As an application of our results, we establish the interior regularity of weak (energy) stable solutions to the problem for the half-Laplacian in dimensions <span>(1 leqslant n leqslant 4)</span>.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"593 - 624"},"PeriodicalIF":1.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269742","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
Systems of differential operators in time-periodic Gelfand–Shilov spaces 时周期格尔方-希洛夫空间中的微分算子系统
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-09-13 DOI: 10.1007/s10231-024-01499-z
Fernando de Ávila Silva, Marco Cappiello, Alexandre Kirilov
{"title":"Systems of differential operators in time-periodic Gelfand–Shilov spaces","authors":"Fernando de Ávila Silva,&nbsp;Marco Cappiello,&nbsp;Alexandre Kirilov","doi":"10.1007/s10231-024-01499-z","DOIUrl":"10.1007/s10231-024-01499-z","url":null,"abstract":"<div><p>This paper explores the global properties of time-independent systems of operators in the framework of time-periodic Gelfand–Shilov spaces. Our main results provide both necessary and sufficient conditions for global solvability and global hypoellipticity, based on analysis of the symbols of operators. We also present a class of time-dependent operators whose solvability and hypoellipticity are linked to the same properties of an associated time-independent system, albeit with a loss of regularity for temporal variables.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"643 - 665"},"PeriodicalIF":1.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142215145","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
Mutual estimates of time-frequency representations and uncertainty principles 时频表示的相互估计和不确定性原理
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-09-12 DOI: 10.1007/s10231-024-01500-9
Angela A. Albanese, Claudio Mele, Alessandro Oliaro
{"title":"Mutual estimates of time-frequency representations and uncertainty principles","authors":"Angela A. Albanese,&nbsp;Claudio Mele,&nbsp;Alessandro Oliaro","doi":"10.1007/s10231-024-01500-9","DOIUrl":"10.1007/s10231-024-01500-9","url":null,"abstract":"<div><p>In this paper we give different estimates between Lebesgue norms of quadratic time-frequency representations. We show that, in some cases, it is not possible to have such bounds in classical <span>(L^p)</span> spaces, but the Lebesgue norm needs to be suitably weighted. This leads to consider weights of polynomial type, and, more generally, of ultradifferentiable type, and this, in turn, gives rise to use as functional setting the ultradifferentiable classes. As applications of such estimates we deduce uncertainty principles both of Donoho-Stark type and of local type for representations.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"667 - 691"},"PeriodicalIF":1.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01500-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142215144","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
Gradient regularity for fully nonlinear equations with degenerate coefficients 具有退化系数的完全非线性方程的梯度正则性
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-09-11 DOI: 10.1007/s10231-024-01498-0
David Jesus, Yannick Sire
{"title":"Gradient regularity for fully nonlinear equations with degenerate coefficients","authors":"David Jesus,&nbsp;Yannick Sire","doi":"10.1007/s10231-024-01498-0","DOIUrl":"10.1007/s10231-024-01498-0","url":null,"abstract":"<div><p>We derive <span>(C^{1,alpha })</span> estimates for viscosity solutions of fully nonlinear equations degenerating on a hypersurface.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"625 - 642"},"PeriodicalIF":1.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688503","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
Sasaki versus Kähler groups 佐佐木与Kähler团体
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-09-11 DOI: 10.1007/s10231-024-01501-8
D. Kotschick, G. Placini
{"title":"Sasaki versus Kähler groups","authors":"D. Kotschick,&nbsp;G. Placini","doi":"10.1007/s10231-024-01501-8","DOIUrl":"10.1007/s10231-024-01501-8","url":null,"abstract":"<div><p>We study fundamental groups of compact Sasaki manifolds and show that compared to Kähler groups, they exhibit rather different behaviour. This class of groups is not closed under taking direct products, and there is often an upper bound on the dimension of a Sasaki manifold realising a given group. The richest class of Sasaki groups arises in dimension 5.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"693 - 709"},"PeriodicalIF":1.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01501-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688484","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
Riemannian curvature identities on almost Calabi–Yau with torsion 6-manifold and generalized Ricci solitons 具有扭转6流形和广义Ricci孤子的几乎Calabi-Yau上的黎曼曲率恒等式
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-08-19 DOI: 10.1007/s10231-024-01494-4
S. Ivanov, N. Stanchev
{"title":"Riemannian curvature identities on almost Calabi–Yau with torsion 6-manifold and generalized Ricci solitons","authors":"S. Ivanov,&nbsp;N. Stanchev","doi":"10.1007/s10231-024-01494-4","DOIUrl":"10.1007/s10231-024-01494-4","url":null,"abstract":"<div><p>It is observed that on a compact almost complex Calabi–Yau with torsion 6-manifold the Nijenhuis tensor is parallel with respect to the torsion connection. If the torsion is closed then the space is a compact generalized gradient Ricci soliton. In this case, the torsion connection is Ricci-flat if and only if either the norm of the torsion or the Riemannian scalar curvature is constant. On a compact almost complex Calabi–Yau with torsion 6-manifold it is shown that the curvature of the torsion connection is symmetric on exchange of the first and the second pairs and has vanishing Ricci tensor if and only if it satisfies the Riemannian first Bianchi identity.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"513 - 542"},"PeriodicalIF":1.0,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688411","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
Toeplitz operators on monomial polyhedra 单项式多面体上的Toeplitz算子
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-08-16 DOI: 10.1007/s10231-024-01495-3
Debraj Chakrabarti, Yanyan Tang, Shuo Zhang
{"title":"Toeplitz operators on monomial polyhedra","authors":"Debraj Chakrabarti,&nbsp;Yanyan Tang,&nbsp;Shuo Zhang","doi":"10.1007/s10231-024-01495-3","DOIUrl":"10.1007/s10231-024-01495-3","url":null,"abstract":"<div><p>Monomial polyhedra are a class of bounded singular Reinhardt domains defined as sublevel sets of holomorphic monomials. In this paper, we completely characterize the <span>(L^p-L^q)</span> boundedness of the Toeplitz operators with radial symbols on monomial polyhedra. This work generalizes the previous results of Toeplitz operators on various generalized Hartogs triangles, as well as extends the recent work of the <span>(L^p)</span> regularity for the Bergman projection on monomial polyhedra.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"543 - 571"},"PeriodicalIF":1.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688365","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
Measure data systems with Orlicz growth 测量数据系统与 Orlicz 的增长
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-08-16 DOI: 10.1007/s10231-024-01489-1
Iwona Chlebicka, Yeonghun Youn, Anna Zatorska-Goldstein
{"title":"Measure data systems with Orlicz growth","authors":"Iwona Chlebicka,&nbsp;Yeonghun Youn,&nbsp;Anna Zatorska-Goldstein","doi":"10.1007/s10231-024-01489-1","DOIUrl":"10.1007/s10231-024-01489-1","url":null,"abstract":"<div><p>We study the existence of very weak solutions to a system </p><div><div><span>$$begin{aligned} {left{ begin{array}{ll}-{pmb {textsf{div}}}{{mathcal {A}}}(x,{D{pmb {textsf{u}}}})=pmb {mathsf {mu }}quad text {in } Omega , pmb {textsf{u}}=0quad text {on } partial Omega end{array}right. } end{aligned}$$</span></div></div><p>with a datum <span>({pmb {mathsf {mu }}})</span> being a vector-valued bounded Radon measure and <span>({{mathcal {A}}}:Omega times {{mathbb {R}}^{ntimes m}}rightarrow {{mathbb {R}}^{ntimes m}})</span> having measurable dependence on the spacial variable and Orlicz growth with respect to the second variable. We are <i>not</i> restricted to the superquadratic case. For the solutions and their gradients we provide regularity estimates in the generalized Marcinkiewicz scale. In addition, we show a precise sufficient condition for the solution to be a Sobolev function.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 1","pages":"407 - 426"},"PeriodicalIF":1.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142215147","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
Maximum principles, ABP estimates and HKS inequalities related to GLE systems 与 GLE 系统有关的最大原则、ABP 估计和 HKS 不等式
IF 1 3区 数学
Annali di Matematica Pura ed Applicata Pub Date : 2024-08-15 DOI: 10.1007/s10231-024-01496-2
Edir Júnior Ferreira Leite, Marcos Montenegro
{"title":"Maximum principles, ABP estimates and HKS inequalities related to GLE systems","authors":"Edir Júnior Ferreira Leite,&nbsp;Marcos Montenegro","doi":"10.1007/s10231-024-01496-2","DOIUrl":"10.1007/s10231-024-01496-2","url":null,"abstract":"<div><p>Closely related to the pioneering work (Berestycki et al. Commun Pure Appl Math, pp 47–92, 1994) by the authors Berestycki, Nirenberg and Varadhan, we prove maximum and comparison principles for generalized Lane-Emden type systems and as consequences we establish Aleksandrov-Bakelman-Pucci estimates and Harnack-Krylov-Safonov inequalities for related non-homogeneous inequalities, among other results. These contributions go towards a comprehensive understanding on strongly coupled nonlinear elliptic systems.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 2","pages":"573 - 592"},"PeriodicalIF":1.0,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688314","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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