{"title":"A Liouville Theorem for Nonlocal Equations in the Heisenberg Group","authors":"E. Cinti","doi":"10.6092/ISSN.2240-2829/5289","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/5289","url":null,"abstract":"We establish a Liouville-type theorem for a subcritical nonlinear problem, involving a fractional power of the sub-Laplacian in the Heisenberg group. To prove our result we will use the local realization of fractional CR covariant operators, which can be constructed as the Dirichlet-to-Neumann operator of a degenerate elliptic equation in the spirit of Caffarelli and Silvestre [8], as established in [14]. The main tools in our proof are the CR inversion and the moving plane method, applied to the solution of the lifted problem in the half-space ℍ n × ℝ + .","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"5 1","pages":"127-146"},"PeriodicalIF":0.2,"publicationDate":"2014-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71263207","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}
{"title":"A Smale Type Result and Applications to Contact Homology","authors":"Vittorio Martino","doi":"10.6092/ISSN.2240-2829/4718","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/4718","url":null,"abstract":"In this note we will show that the injection of a suitable subspace of the space of Legendrian loops into the full loop space is an S 1 -equivariant homotopy equivalence. Moreover, since the smaller space is the space of variations of a given action functional, we will compute the relative Contact Homology of a family of tight contact forms on the three-dimensional torus.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"5 1","pages":"45-56"},"PeriodicalIF":0.2,"publicationDate":"2014-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71263114","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}
{"title":"Parabolic Problems with Dynamic Boundary Conditions in L p Spaces","authors":"D. Guidetti","doi":"10.6092/ISSN.2240-2829/4719","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/4719","url":null,"abstract":"We illustrate a maximal regularity result for parabolic problems with dynamic boundary conditions in L p spaces.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"5 1","pages":"57-66"},"PeriodicalIF":0.2,"publicationDate":"2014-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71263158","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}
{"title":"L p - Liouville theorems for invariant evolution equations","authors":"A. Kogoj","doi":"10.6092/ISSN.2240-2829/4674","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/4674","url":null,"abstract":"Some Liouville-type theorems in Lebesgue spaces for several classes of evolution equations are presented. The involved operators are left invariant with respect to Lie group composition laws. Results for both solutions and sub-solutions are given.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"5 1","pages":"1-14"},"PeriodicalIF":0.2,"publicationDate":"2014-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71263381","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}
{"title":"Algebras of Complete Hörmander Vector Fields, and Lie-Group Construction","authors":"A. Bonfiglioli","doi":"10.6092/ISSN.2240-2829/4707","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/4707","url":null,"abstract":"The aim of this note is to characterize the Lie algebras g of the analytic vector fields in R N which coincide with the Lie algebras of the (analytic) Lie groups defined on R N (with its usual differentiable structure). We show that such a characterization amounts to asking that: (i) g is N-dimensional; (ii) g admits a set of Lie generators which are complete vector fields; (iii) g satisfies Hormander’s rank condition. These conditions are necessary, sufficient and mutually independent. Our approach is constructive, in that for any such g we show how to construct a Lie group G = (R N , *) whose Lie algebra is g. We do not make use of Lie’s Third Theorem, but we only exploit the Campbell-Baker-Hausdorff-Dynkin Theorem for ODE’s.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"5 1","pages":"15-30"},"PeriodicalIF":0.2,"publicationDate":"2014-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71263406","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}
{"title":"Reconstruction of a convolution kernel in a parabolic problem with a memory term in the boundary conditions","authors":"D. Guidetti","doi":"10.6092/ISSN.2240-2829/4154","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/4154","url":null,"abstract":"We consider the problem of the reconstruction of the convolution kernel, together with the solution, in a semilinear integrodiential parabolic problem in the case that in the boundary conditions, there appear quite general memory operators.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"4 1","pages":"47-55"},"PeriodicalIF":0.2,"publicationDate":"2013-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71262844","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}
{"title":"LANZANI-STEIN INEQUALITIES IN HEISENBERG GROUPS","authors":"A. Baldi","doi":"10.6092/ISSN.2240-2829/4153","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/4153","url":null,"abstract":"Lanzani & Stein consider a class of div-curl inequalities in de Rham's complex. In this note we examine the natural counterpart of that kind of inequalities for dierential forms in Heisenberg groups H1 and H2.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"4 1","pages":"56-75"},"PeriodicalIF":0.2,"publicationDate":"2013-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71262770","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}
{"title":"Direct and inverse problems for linear relations","authors":"A. Favini","doi":"10.6092/ISSN.2240-2829/4157","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/4157","url":null,"abstract":"Direct and inverse problem related to linear differential inclusions in Banach spaces are studied.The abstract results are applied to degenerate partial dierential equations of parabolic type.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"4 1","pages":"1-14"},"PeriodicalIF":0.2,"publicationDate":"2013-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71262897","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}