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Bruno Pini Mathematical Analysis Seminar最新文献

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Some relations between fractional Laplace operators and Hessian operators 分数阶拉普拉斯算子与黑森算子的若干关系
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2011-12-31 DOI: 10.6092/ISSN.2240-2829/2668
F. Ferrari
{"title":"Some relations between fractional Laplace operators and Hessian operators","authors":"F. Ferrari","doi":"10.6092/ISSN.2240-2829/2668","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/2668","url":null,"abstract":"After recalling the many representations of the fractional Laplace operator and some of its important properties, some recent results (proved in a joint work with Bruno Franchi and Igor Verbitsky) about the relations between the k-Hessian energy of the k-Hessian operator of a k convex function vanishing at infinity and the fractional energy of a particular fractional operator will be introduced. Moreover we shall recall an integration by parts formula for the fractional Laplace operator giving a new simpler proof.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"2 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2011-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71262278","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
Differential forms in Carnot groups: a variational approach 卡诺群的微分形式:变分方法
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2011-12-31 DOI: 10.6092/ISSN.2240-2829/2664
A. Baldi
{"title":"Differential forms in Carnot groups: a variational approach","authors":"A. Baldi","doi":"10.6092/ISSN.2240-2829/2664","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/2664","url":null,"abstract":"Carnot groups (connected simply connected nilpotent stratified Lie groups) can be endowed with a complex of ``intrinsic'' differential forms. In this paper we want to provide an evidence of the intrinsic character of Rumin's complex, in the spirit of the Riemannian approximation, like in e.g., the notes of Gromov (Textes Mathematiques 1981) and in Rumin (Geom. Funct. Anal.,2000) . More precisely, we want to show that the intrinsic differential is a limit of suitably weighted usual first order de Rham differentials. As an application, we prove that the L^2-energies associated to classical Maxwell's equations in R^n Gamma-converges to the L^2-energies associated to an ''intrinsic'' Maxwell's equation in a free Carnot group.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"2 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2011-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71262070","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
Decadimento uniforme per equazioni integro-differenziali lineari di Volterra 沃尔泰拉线性积分微分方程的均匀衰变
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2011-12-31 DOI: 10.6092/ISSN.2240-2829/2669
Stefania Gatti
{"title":"Decadimento uniforme per equazioni integro-differenziali lineari di Volterra","authors":"Stefania Gatti","doi":"10.6092/ISSN.2240-2829/2669","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/2669","url":null,"abstract":"This talk is devoted to some recent results concerning the exponential and the polynomial decays of the energy associated with a linear Volterra integro-differential equation of hyperbolic type in a Hilbert space, which is an abstract version of the equation describing the motion of a linearly viscoelastic solid occupying a (bounded) volume at rest. We provide sufficient conditions for the decay to hold, without invoking differential inequalities involving the convolution kernel. A similar analysis is carried on in the whole N-dimensional real space, although both the polynomial and the exponential decay of the memory kernel lead to a polynomial decay of the energy, with a rate influenced by the space dimension N. These results are contained in two joint papers with Monica Conti and Vittorino Pata (Politecnico di Milano).","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"2 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2011-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71262294","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
Hypoellipticity and Non Hypoellipticity for Sums of Squares of Complex Vector Fields 复向量场平方和的亚椭圆性和非亚椭圆性
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2011-12-31 DOI: 10.6092/ISSN.2240-2829/2665
A. Bove
{"title":"Hypoellipticity and Non Hypoellipticity for Sums of Squares of Complex Vector Fields","authors":"A. Bove","doi":"10.6092/ISSN.2240-2829/2665","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/2665","url":null,"abstract":"In this talk we give a report on a paper where we consider a model sum of squares of planar complex vector fields, being close to Kohn's operator but with a point singularity. The characteristic variety of the operator is the same symplectic real analytic manifold as Kohn's. We show that this operator is hypoelliptic and Gevrey hypoelliptic provided certain conditions are satisfied. We show that in the Gevrey spaces below a certain index the operator is not hypoelliptic. Moreover there are cases in which the operator is not even hypoelliptic. This fact leads to some general negative statement on the hypoellipticity properties of sums of squares of complex vector fields, even when the complex H\"ormander condition is satisfied.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"2 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2011-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71262125","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: 6
Un nuovo approccio alle disuguaglianze isoperimetriche quantitative 一种解决定量等距不平等的新方法
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2011-12-31 DOI: 10.6092/ISSN.2240-2829/2671
G. Leonardi
{"title":"Un nuovo approccio alle disuguaglianze isoperimetriche quantitative","authors":"G. Leonardi","doi":"10.6092/ISSN.2240-2829/2671","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/2671","url":null,"abstract":"We introduce a new variational method for studying geometric and functional inequalities with quantitative terms. In the context of isoperimetric-type inequalities, this method (called Selection Principle) is based on a penalization technique combined with the regularity theory of quasiminimizers of the perimeter functional. In this seminar we present the method and describe two remarkable applications. The rst one is a new proof of the sharp quantitative isoperimetric inequality in Rn. The second one is the proof of a conjecture posed by Hall about the optimal constant in the quantitative isoperimetric inequality in R2, in the small asymmetry regime.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"2 1","pages":"1-15"},"PeriodicalIF":0.2,"publicationDate":"2011-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71262945","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
Sulla simmetria delle soluzioni stabili di alcune equazioni semilineari 一些半线性方程的稳定解的对称性
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2010-12-30 DOI: 10.6092/ISSN.2240-2829/2253
F. Ferrari
{"title":"Sulla simmetria delle soluzioni stabili di alcune equazioni semilineari","authors":"F. Ferrari","doi":"10.6092/ISSN.2240-2829/2253","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/2253","url":null,"abstract":"Con particolare riferimento alle proprieta di simmetria, si discutera del comportamento delle soluzioni stabili di alcune equazioni a derivate parziali semilineari ellittiche. Verranno inoltre presentate alcune disuguaglianze pesate di tipo Poincare; ottenute a partire da campi vettoriali che commutano con l'operatore.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2010-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71262113","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
I Teoremi di Campbell, Baker, Hausdorff e Dynkin. Storia, Prove, Problemi Aperti 坎贝尔，贝克，豪斯多夫和戴金的定理。历史，证据，未解决的问题
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2010-12-30 DOI: 10.6092/ISSN.2240-2829/2256
Antonio Bonfiglioli
{"title":"I Teoremi di Campbell, Baker, Hausdorff e Dynkin. Storia, Prove, Problemi Aperti","authors":"Antonio Bonfiglioli","doi":"10.6092/ISSN.2240-2829/2256","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/2256","url":null,"abstract":"The aim of this lecture is to provide an overview of facts and references about past and recent results on the Theorem of Campbell, Baker, Hausdorff and Dynkin (shortcut as the CBHD Theorem), following the recent preprint monograph [13]. In particular, we shall give sketches of the following facts: A historical precis of the early proofs (see also [1]); the statement of the CBHD Theorem as usually given in Algebra and that employed in the Analysis of linear PDE’s; a review of proofs of the CBHD Theorem (as given by: Bourbaki; Hausdorff; Dynkin; Varadarajan) together with a unifying demonstrational approach; an application to the Third Theorem of Lie (in local form). Some new results will be also commented: The intertwinement of the CBHD Theorem with the Theorem of Poincare-Birkhoff-Witt and with the free Lie algebras (see [12]); recent results on optimal domains of convergence.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2010-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71262334","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
Capacità d'insiemi su alberi, grafi e spazi metrici Ahlfors-regolari 在树木、图形和均匀的几何空间上的干扰能力
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2010-12-30 DOI: 10.6092/ISSN.2240-2829/2257
Nicola Arcozzi
{"title":"Capacità d'insiemi su alberi, grafi e spazi metrici Ahlfors-regolari","authors":"Nicola Arcozzi","doi":"10.6092/ISSN.2240-2829/2257","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/2257","url":null,"abstract":"Work in collaboration with R. Rochberg E. Sawyer and B. Wick [ARSW]. We show that the potential theory of Bessel-type kernels on Ahlfors-regular metric spaces is equivalent, in a precise sense, to potential theory on trees. The basis of this work was in [ARS2], where the relationship between discrete potential theory and some classical function theory was considered. Some applications [Ar] to estimation of sets' and condenser's capacity are discussed.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"58 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2010-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71262385","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
Risultati di perturbazione per operatori lineari multivoci ed applicazioni 多价线性操作符和应用程序的扰动结果
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2010-12-30 DOI: 10.6092/ISSN.2240-2829/2226
A. Favini
{"title":"Risultati di perturbazione per operatori lineari multivoci ed applicazioni","authors":"A. Favini","doi":"10.6092/ISSN.2240-2829/2226","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/2226","url":null,"abstract":"Pertubation results for generators of infinitely differentiable semigroups of linear operators are given. Some application to partial differential equations are described.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2010-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71262447","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
Una Trasformata di Legendre su un modello non standard 传奇在非标准模型上的变换
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2010-12-30 DOI: 10.6092/ISSN.2240-2829/2229
V. Martino
{"title":"Una Trasformata di Legendre su un modello non standard","authors":"V. Martino","doi":"10.6092/ISSN.2240-2829/2229","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/2229","url":null,"abstract":"We consider an exotic contact form on the three-dimensional sphere and we establish explicitly the existence of a non singular vector field in its kernel such that the dual form is still a contact form with the same orientation than the given one. In particular this means that a Legendre transform can be completed.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2010-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71262049","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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