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Maximum principles for viscosity solutions of weakly elliptic equations 弱椭圆型方程粘性解的极大值原理
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2019-12-31 DOI: 10.6092/ISSN.2240-2829/10395
A. Vitolo
{"title":"Maximum principles for viscosity solutions of weakly elliptic equations","authors":"A. Vitolo","doi":"10.6092/ISSN.2240-2829/10395","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/10395","url":null,"abstract":"Maximum principles play an important role in the theory of elliptic equations. In the last decades there have been many contributions related to the development of fully nonlinear equations and viscosity solutions. Here we consider degenerate elliptic equations, where the main term  is a partial trace of the Hessian matrix of the solution. We establish maximum principles in domains that are unbounded in some directions, contained in slabs, and extended  maximum principles, which lead to removable singularity results.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"10 1","pages":"110-136"},"PeriodicalIF":0.2,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47538882","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
On s-harmonic functions on cones 关于锥上的s调和函数
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2019-12-31 DOI: 10.6092/ISSN.2240-2829/10366
S. Vita
{"title":"On s-harmonic functions on cones","authors":"S. Vita","doi":"10.6092/ISSN.2240-2829/10366","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/10366","url":null,"abstract":"We deal with non negative functions which are s-harmonic on a given cone of the n-dimensional Euclidean space with vertex at zero, vanishing on the complementary. We consider the case when the parameter s approaches 1, wondering whether solutions of the problem do converge to harmonic functions in the same cone or not. Surprisingly, the answer will depend on the opening of the cone through an auxiliary eigenvalue problem on the upper half sphere. These conic functions are involved in the study of the nodal regions in the case of optimal partitions and other free boundary problems and play a crucial role in the extension of the Alt-Caffarelli-Friedman monotonicity formula to the case of fractional diffusions.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"10 1","pages":"28-41"},"PeriodicalIF":0.2,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48689910","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
Radial solutions of Lane-Emden-Fowler equations with Pucci's extremal operators 带Pucci极值算子的Lane-Emden-Fowler方程的径向解
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2019-12-31 DOI: 10.6092/ISSN.2240-2829/10360
F. Leoni
{"title":"Radial solutions of Lane-Emden-Fowler equations with Pucci's extremal operators","authors":"F. Leoni","doi":"10.6092/ISSN.2240-2829/10360","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/10360","url":null,"abstract":"We report on some recent results obtained for positive radial solutions of Lane-Emden-Fowler type equations with Pucci's operators as principal parts. The presented results include the asymptotic analysis of almost critical solutions in the unit ball,  existence results in annular domains and sharp Liouville-type results for exterior Dirichlet problems.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"10 1","pages":"1-13"},"PeriodicalIF":0.2,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45378847","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
The stickiness phenomena of nonlocal minimal surfaces: new results and a comparison with the classical case 非局部极小曲面的粘滞现象:新结果及与经典情况的比较
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2019-11-29 DOI: 10.6092/issn.2240-2829/10362
Claudia Bucur
{"title":"The stickiness phenomena of nonlocal minimal surfaces: new results and a comparison with the classical case","authors":"Claudia Bucur","doi":"10.6092/issn.2240-2829/10362","DOIUrl":"https://doi.org/10.6092/issn.2240-2829/10362","url":null,"abstract":"We discuss in this note the stickiness phenomena for nonlocal minimal surfaces. Classical minimal surfaces in convex domains do not stick to the boundary of the domain, hence examples of stickiness can be obtained only by removing the assumption of convexity. On the other hand, in the nonlocal framework, stickiness is ''generic''.  We provide various examples from the literature, and focus  on the case of complete stickiness in highly nonlocal regimes.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"10 1","pages":"42-82"},"PeriodicalIF":0.2,"publicationDate":"2019-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47017293","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
W 2,p a priori estimates for nonvariational operators: the sharp maximal function technique 非变量算子的W2，p先验估计：sharp极大函数技术
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2018-12-31 DOI: 10.6092/issn.2240-2829/8939
M. Bramanti
{"title":"W 2,p a priori estimates for nonvariational operators: the sharp maximal function technique","authors":"M. Bramanti","doi":"10.6092/issn.2240-2829/8939","DOIUrl":"https://doi.org/10.6092/issn.2240-2829/8939","url":null,"abstract":"We consider a nonvariational degenerate elliptic operator, structured on a system of left invariant, 1-homogeneous, Hormander vector fields on a Carnot group, where the coefficient matrix is symmetric, uniformly positive on a bounded domain and the coefficients are locally VMO. We discuss a new proof (given in [BT] and also based on results in [BF]) of the interior estimates in Sobolev spaces, first proved in [BB-To]. The present proof extends to this context Krylov' technique, introduced in [K1], consisting in estimating the sharp maximal function of second order derivatives.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"9 1","pages":"1-19"},"PeriodicalIF":0.2,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49374570","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
The regularity problem for geodesics of the control distance 控制距离测地线的正则性问题
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2018-12-31 DOI: 10.6092/ISSN.2240-2829/8969
R. Monti
{"title":"The regularity problem for geodesics of the control distance","authors":"R. Monti","doi":"10.6092/ISSN.2240-2829/8969","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/8969","url":null,"abstract":"In this survey, we present some recent results on the problem about the regularity of length-minimizing curves in sub-Riemannian geometry. We also sketch the possible application of some ideas coming from Geometric Measure Theory.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"9 1","pages":"137-146"},"PeriodicalIF":0.2,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42127403","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
LOCAL BOUNDEDNESS OF VECTORIAL MINIMIZERS OF NON-CONVEX FUNCTIONALS 非凸泛函的向量极小化子的局部有界性
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2018-12-31 DOI: 10.6092/ISSN.2240-2829/8942
G. Cupini, M. Focardi, F. Leonetti, E. Mascolo
{"title":"LOCAL BOUNDEDNESS OF VECTORIAL MINIMIZERS OF NON-CONVEX FUNCTIONALS","authors":"G. Cupini, M. Focardi, F. Leonetti, E. Mascolo","doi":"10.6092/ISSN.2240-2829/8942","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/8942","url":null,"abstract":"We prove a local boundedness result for local minimizers of a class of non-convex functionals, under special structure assumptions on the energy density. The proof follows the lines of that in [CupLeoMas17], where a similar result is proved under slightly stronger assumptions on the energy density.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"9 1","pages":"20-40"},"PeriodicalIF":0.2,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48440245","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
Critical exponents and where to find them 关键指数和在哪里找到它们
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2018-12-31 DOI: 10.6092/ISSN.2240-2829/8948
S. Lucente
{"title":"Critical exponents and where to find them","authors":"S. Lucente","doi":"10.6092/ISSN.2240-2829/8948","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/8948","url":null,"abstract":"In this expository paper we present a list of different semilinear wave-type problems with time-variable coefficients. The aim of this work is to understand the influence of such coefficients on the critical exponents for polynomial nonlinearities. Statements of global existence and blow-up will follow according to exponents which are below or above these critical ones.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"9 1","pages":"102-114"},"PeriodicalIF":0.2,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42555121","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: 5
The method of moving planes: a quantitative approach 移动平面的方法:定量方法
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2018-11-13 DOI: 10.6092/ISSN.2240-2829/8944
Giulio Ciraolo, Alberto Roncoroni
{"title":"The method of moving planes: a quantitative approach","authors":"Giulio Ciraolo, Alberto Roncoroni","doi":"10.6092/ISSN.2240-2829/8944","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/8944","url":null,"abstract":"We review classical results where the method of the moving planes has been used to prove symmetry properties for overdetermined PDE's boundary value problems (such as Serrin's overdetermined problem) and for rigidity problems in geometric analysis (like Alexandrov soap bubble Theorem), and we give an overview of some recent results related to quantitative studies of the method of moving planes, where quantitative approximate symmetry results are obtained.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"9 1","pages":"41-77"},"PeriodicalIF":0.2,"publicationDate":"2018-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47511796","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: 9
Time Fractional Derivatives and Evolution Equations 时间分数阶导数与演化方程
IF 0.2
Bruno Pini Mathematical Analysis Seminar Pub Date : 2018-05-31 DOI: 10.6092/ISSN.2240-2829/8167
D. Guidetti
{"title":"Time Fractional Derivatives and Evolution Equations","authors":"D. Guidetti","doi":"10.6092/ISSN.2240-2829/8167","DOIUrl":"https://doi.org/10.6092/ISSN.2240-2829/8167","url":null,"abstract":"In this seminar we introduce the fractional derivatives of Riemann-Liouville and Caputo, with some of their main properties. We conclude by illustrating certain results of maximal regularity for mixed initial-boundary value problems, evolving them.","PeriodicalId":41199,"journal":{"name":"Bruno Pini Mathematical Analysis Seminar","volume":"8 1","pages":"142-152"},"PeriodicalIF":0.2,"publicationDate":"2018-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49039002","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: 1
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