Geometric Properties for Parabolic and Elliptic PDE's (eBook)

This book contains the contributions resulting from the 6th Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDEs, which was held in Cortona (Italy) during the week of May 20-24, 2019. This book will be of great interest for the mathematical community and in particular for researchers studying parabolic and elliptic PDEs. It covers many different fields of current research as follows: convexity of solutions to PDEs, qualitative properties of solutions to parabolic equations, overdetermined problems, inverse problems, Brunn-Minkowski inequalities, Sobolev inequalities, and isoperimetric inequalities.

Tatsuki Kawakami has been a professor of the Faculty of Advanced Science and Technology at Ryukoku University since 2019. He is interested in research fields such as elliptic and parabolic PDEs, the existence of solutions and their asymptotic behavior, dynamic boundary problems, and related topics.

Paolo Salani is a full professor of Mathematical Analysis at Dipartimento di Matematica e Informatica 'U. Dini' of Università degli Studi di Firenze. His main research interests concern the study of geometric properties (such as convexity, starshape, etc.) of solutions to elliptic and parabolic PDEs, overdetermined problems, geometric and analytic inequalities of isoperimetric flavor, convex geometry and analysis.

Futoshi Takahashi has been a professor in the Department of Mathematics at Osaka City University since 2009. He has been interested in research fields such as variational methods, functional inearities, and related nonlinear PDEs.