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Bruno Pini Mathematical Analysis Seminar最新文献

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Symmetry and rigidity results for composite membranes and plates 对称和刚性导致复合膜和板
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2020-03-28 DOI: 10.6092/ISSN.2240-2829/10587
E. Vecchi
{"title":"Symmetry and rigidity results for composite membranes and plates","authors":"E. Vecchi","doi":"10.6092/ISSN.2240-2829/10587","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/10587","url":null,"abstract":"The composite membrane problem is an eigenvalue optimization problem deeply studied from the beginning of the '00's. In this note we survey most of the results proved by several authors over the last twenty years, up to the recent paper [14] written in collaboration with Giovanni Cupini.We finally introduce an eigenvalue optimization problem for a fourth order operator, called composite plate problem and we present the symmetry and rigidity results obtained in this framework. These last mentioned results are part of the papers [12,13], written in collaboration with Francesca Colasuonno.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"11 1","pages":"157-174"},"PeriodicalIF":0.2,"publicationDate":"2020-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46625253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hilbert-Haar coordinates and Miranda's theorem in Lie groups 李群中的Hilbert-Haar坐标和Miranda定理
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2020-03-28 DOI: 10.6092/ISSN.2240-2829/10582
A. Domokos, J. Manfredi
{"title":"Hilbert-Haar coordinates and Miranda's theorem in Lie groups","authors":"A. Domokos, J. Manfredi","doi":"10.6092/ISSN.2240-2829/10582","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/10582","url":null,"abstract":"We study the interior regularity of solutions to a class of quasilinear equations of non-degenerate p-Laplacian type on Lie groups that admit a system of Hilbert-Haar coordinates. These are coordinates with respect to which every linear function has zero symmetrized second order horizontal derivatives. All Carnot groups of rank two are in this category, as well as the Engel group, the Goursat type groups, and those general Carnot groups of step three for which the non-zero commutators of order three are linearly independent.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"11 1","pages":"94-118"},"PeriodicalIF":0.2,"publicationDate":"2020-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49544723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
(Non)local γ-convergence γ-convergenza (non)locale （非）局部γ-收敛γ-收敛（非）本地
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2020-03-28 DOI: 10.6092/ISSN.2240-2829/10580
S. Dipierro, Pietro Miraglio, E. Valdinoci
{"title":"(Non)local γ-convergence γ-convergenza (non)locale","authors":"S. Dipierro, Pietro Miraglio, E. Valdinoci","doi":"10.6092/ISSN.2240-2829/10580","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/10580","url":null,"abstract":"We present some long-range interaction models for phase coexistence which have recently appeared in the literature, recalling also their relation to classical interface and capillarity problems. In this note, the main focus will be on the Γ-convergence methods, emphasizing similarities and differences between the classical theory and the new trends of investigation. In doing so, we also obtain some new, more precise Γ-convergence results in terms of ``interior'' and ``exterior'' contributions. We also discuss the structural differences between Γ-limits and ``pointwise'' limits, especially concerning the ``boundary terms''.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"11 1","pages":"68-93"},"PeriodicalIF":0.2,"publicationDate":"2020-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41840992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Regularity for quasilinear PDEs in Carnot groups via Riemannian approximation 卡诺群拟线性偏微分方程的黎曼近似正则性
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2020-03-28 DOI: 10.6092/ISSN.2240-2829/10589
A. Domokos, J. Manfredi
{"title":"Regularity for quasilinear PDEs in Carnot groups via Riemannian approximation","authors":"A. Domokos, J. Manfredi","doi":"10.6092/ISSN.2240-2829/10589","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/10589","url":null,"abstract":"We study the interior regularity of weak solutions to subelliptic quasilinear PDEs in Carnot groups of the formΣi=1m1Xi (Φ(|∇Hu|2)Xiu) = 0.Here ∇Hu = (X1u,...,Xmiu) is the horizontal gradient, δ > 0 and the exponent p ∈ [2, p*), where p* depends on the step ν and the homogeneous dimension Q of the group, and it is given byp* = min {2ν ∕ ν-1 , 2Q+8 ∕ Q-2}.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"11 1","pages":"119-142"},"PeriodicalIF":0.2,"publicationDate":"2020-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44379309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimization of nonlinear eigenvalues under measure or perimeter constraint 测量或周长约束下非线性特征值的优化
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2020-01-01 DOI: 10.6092/ISSN.2240-2829/12299
Mazzoleni Dario
{"title":"Optimization of nonlinear eigenvalues under measure or perimeter constraint","authors":"Mazzoleni Dario","doi":"10.6092/ISSN.2240-2829/12299","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/12299","url":null,"abstract":"In this paper we recall some recent results about variational eigenvalues of the p-Laplacian, we show new applications and point out some open problems. We focus on the continuity properties of the eigenvalues under the gamma_p-convergence of capacitary measures, which are needed to prove existence results for the minimization of nonlinear eigenvalues in the class of p-quasi open sets contained in a box under a measure constraint. Finally, the new contribution of this paper is to show that these continuity results can be employed to prove existence of minimizers for nonlinear eigenvalues among measurable sets contained in a box and under a perimeter constraint.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"11 1","pages":"30-46"},"PeriodicalIF":0.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71262372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Degenerate differential problems with fractional derivatives 分数阶导数的退化微分问题
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2020-01-01 DOI: 10.6092/ISSN.2240-2829/12300
M. Horani, A. Favini
{"title":"Degenerate differential problems with fractional derivatives","authors":"M. Horani, A. Favini","doi":"10.6092/ISSN.2240-2829/12300","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/12300","url":null,"abstract":"We describe an extension of previous results on degenerate abstract equations described by Favini and Yagi in their monograph cited in the references.This allows us to study degenerate differential equations with fractional derivative in time. Both direct and relative inverse problems are studied. Finally, various applications to degenerate partial differential equations are described.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"11 1","pages":"47-68"},"PeriodicalIF":0.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71262409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Another look to the orthotropic functional in the plane 另一个平面上的正交各向异性泛函
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2020-01-01 DOI: 10.6092/ISSN.2240-2829/12160
P. Bousquet
{"title":"Another look to the orthotropic functional in the plane","authors":"P. Bousquet","doi":"10.6092/ISSN.2240-2829/12160","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/12160","url":null,"abstract":"We address the C1 regularity of the Lipschitz minimizers to the orthotropic functional in the plane.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"11 1","pages":"1-29"},"PeriodicalIF":0.2,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71262252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
The nodal set of solutions to anomalous equations 反常方程解的节点集
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2019-12-31 DOI: 10.6092/ISSN.2240-2829/10367
Giorgio Tortone
{"title":"The nodal set of solutions to anomalous equations","authors":"Giorgio Tortone","doi":"10.6092/ISSN.2240-2829/10367","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/10367","url":null,"abstract":"This note focuses on the geometric-theoretic analysis of the nodal set of solutions to specific degenerate or singular equations. As they belong to the Muckenhoupt class A_2, these operators appear in the seminal works of Fabes, Kenig, Jerison and Serapioni. In particular, they have recently attracted a lot of attention in the last decade due to their link to the local realization of the fractional Laplacian. The  goal is to get a glimpse of the complete theory of the nodal set of solutions of such equations in the spirit of the seminal works of Hardt, Simon, Han and Lin.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"10 1","pages":"98-109"},"PeriodicalIF":0.2,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44361582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Large sets at infinity and Maximum Principle on unbounded domains for a class of sub-elliptic operators 无穷大集与一类亚椭圆算子无界域上的极大值原理
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2019-12-31 DOI: 10.6092/ISSN.2240-2829/10364
Stefano Biagi
{"title":"Large sets at infinity and Maximum Principle on unbounded domains for a class of sub-elliptic operators","authors":"Stefano Biagi","doi":"10.6092/ISSN.2240-2829/10364","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/10364","url":null,"abstract":"Maximum Principles on unbounded domains play a crucial role in several problems related to linear second-order PDEs of elliptic and parabolic type. In the present notes, based on a joint work with prof. E. Lanconelli, we consider a class of sub-elliptic operators L in R^N and we establish some criteria for an unbounded open set to be a Maximum Principle set for L. We extend some classical results related to the Laplacian(proved by Deny, Hayman and Kennedy) and to the sub-Laplacians on homogeneous Carnot groups (proved by Bonfiglioli and Lanconelli).","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"10 1","pages":"83-97"},"PeriodicalIF":0.2,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44223980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sobolev-Poincaré inequalities for differential forms and currents 微分形式和电流的Sobolev Poincaré不等式
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2019-12-31 DOI: 10.6092/ISSN.2240-2829/10361
A. Baldi
{"title":"Sobolev-Poincaré inequalities for differential forms and currents","authors":"A. Baldi","doi":"10.6092/ISSN.2240-2829/10361","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/10361","url":null,"abstract":"In this note we collect some results in R^n about (p,q) Poincare and Sobolev inequalities for differential forms obtained in a joint research with Franchi and Pansu. In particular, we focus to the case p=1. From the geometric point of view, Poincare and Sobolev inequalities for differential forms provide a quantitative formulation of the vanishing of the cohomology. As an application of the results obtained in the case p=1 we obtain  Poincare and Sobolev inequalities for Euclidean currents.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"10 1","pages":"14-27"},"PeriodicalIF":0.2,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43729056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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