Ph.D. and Young Researchers Seminars at University of Padova
Ph.D. and Young Researchers Seminars at University of Padova
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The main aim of Mic Seminars is to bring together young mathematicians from different universities. It provides an informal context to share knowledge and ideas, and to build social networks within the different mathematical communities.
Speaker: Lorenzo Braglia (Università degli Studi di Parma)
Title: Global Hölder regularity for eigenvalue-type equations on irregular domains
Abstract: Are Dirichlet eigenfunctions of the N-Laplacian globally Hölder continuous on contractible domains of finite inradius, i.e. containing no arbitrarily large balls? We give a positive answer through higher gradient integrability for weak solutions to nonlinear PDEs in divergence form, under suitable geometric assumptions. In the critical case p=N, higher integrability alone suffices on Lipschitz domains. On irregular domains, the key is to preserve the zero boundary condition at the improved exponent. Morrey's embedding applied to the zero extension then yields global Hölder continuity up to the boundary. Joint work with L. Brasco.
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