Bruno Pini Mathematical Analysis Seminar 2023-01-09T11:40:18+01:00 Annamaria Montanari Open Journal Systems <strong>Bruno Pini Mathematical Analysis Seminar (BPMAS) – ISSN 2240-2829</strong> publishes seminars solicited by the Department of Mathematics, University of Bologna. It features recent developments in mathematical analysis. A basis of resolutive sets for the heat equation: an elementary construction 2023-01-05T16:18:37+01:00 Alessia E. Kogoj Ermanno Lanconelli <p>By an easy “trick” taken from the caloric polynomial theory, we prove the existence of a basis of the Euclidean topology whose elements are resolutive sets of the heat equation. This result can be used to construct, with a very elementary approach, the Perron solution of the caloric Dirichlet problem on arbitrary bounded open subsets of the Euclidean space-time.</p> 2023-01-09T00:00:00+01:00 Copyright (c) 2022 Alessia E. Kogoj, Ermanno Lanconelli New concentration phenomena for radial sign-changing solutions of fully nonlinear elliptic equations 2023-01-05T16:38:18+01:00 Fabiana Leoni <p>We present recent results about radial sign-changing solutions of a class of fully nonlinear elliptic Dirichlet problems posed in a ball, driven by the extremal Pucci's operators and provided with power zero order terms. We show that new critical exponents appear, related to the existence or nonexistence of sign-changing solutions and due to the fully nonlinear character of the considered problem. Furthermore, we analyze the new concentration phenomena occurring as the exponents approach the critical values. <br><br></p> 2023-01-09T00:00:00+01:00 Copyright (c) 2022 Fabiana Leoni The basic problem of the calculus of variations: Du Bois-Reymond equation, regularity of minimizers and of minimizing sequences 2023-01-05T17:04:09+01:00 Piernicola Bettiol Carlo Mariconda <p>We consider the basic problem of the Calculus of variations of minimizing an integral functional among the absolutely continuous functions that satisfy prescribed boundary conditions. We resume the state of the art and our recent contributions concerning the validity of the Du Bois-Reymond condition, and the Lipschitz regularity of the minimizers and of minimizing sequences (e.g., Lavrentiev phenomenon).</p> 2023-01-09T00:00:00+01:00 Copyright (c) 2022 Piernicola Bettiol, Carlo Mariconda On weighted second order Adams inequalities with Navier boundary conditions 2023-01-05T17:42:02+01:00 Federica Sani <p>We obtain some sharp weighted version of Adams' inequality on second order Sobolev spaces with Navier boundary conditions. The weights that we consider determine a supercritical exponential growth, except in the origin, and the corresponding inequalities hold on <em>radial</em> functions only. We also consider the problem of extremal functions, and we show that the sharp suprema are achieved, as in the unweighted classical case.</p> 2023-01-09T00:00:00+01:00 Copyright (c) 2022 Federica Sani The sub-Finsler Bernstein problem in H1 2023-01-05T18:06:26+01:00 Gianmarco Giovannardi <p>This is a note based on the paper [32] written in collaboration with M. Ritoré. The purpose of this note is to present and discuss the Bernstein type problems in the sub-Finsler Heisenberg group H<sup>1</sup>. We give a general idea of the state of the art and we prove that a complete, stable, (X,Y)-Lipschitz surface is a vertical plane.</p> 2023-01-09T00:00:00+01:00 Copyright (c) 2022 Gianmarco Giovannardi On the regularity of the solutions and of analytic vectors for “sums of squares” 2023-01-05T19:01:45+01:00 Gregorio Chinni <p>We present a brief survey on some recent results concerning the local and global regularity of the solutions for some classes/models of sums of squares of vector fields with real-valued real analytic coefficients of H"ormander type. Moreover we also illustrate a result concerning the microlocal Gevrey regularity of analytic vectors for operators sums of squares of vector fields with real-valued real analytic coefficients of H"ormander type, thus providing a microlocal version, in the analytic category, of a result due to M. Derridj.</p> 2023-01-09T00:00:00+01:00 Copyright (c) 2022 Gregorio Chinni