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.

Autorentext
Vincenzo Ferone is a full professor of Mathematical Analysis at Dipartimento di Matematica e Applicazioni "R. Caccioppoli" of Università di Napoli Federico II. His main research interests concern various topics in the calculus of variations and in the theory of partial differential equations, such as optimization problems on classes of equimeasurable functions, comparison results for solutions to PDEs, optimization, existence and regularity for solutions to PDEs, 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.

Inhalt
- Poincaré and Hardy Inequalities on Homogeneous Trees. - Ground State Solutions for the Nonlinear Choquard Equation with Prescribed Mass. - Optimization of the Structural Performance of Non-homogeneous Partially Hinged Rectangular Plates. - Energy-Like Functional in a Quasilinear Parabolic Chemotaxis System. - Solvability of a Semilinear Heat Equation via a Quasi Scale Invariance. - Bounds for Sobolev Embedding Constants in Non-simply Connected Planar Domains. - Sharp Estimate of the Life Span of Solutions to the Heat Equation with a Nonlinear Boundary Condition. - Neutral Inclusions, Weakly Neutral Inclusions, and an Over-determined Problem for Confocal Ellipsoids. - Nonexistence of Radial Optimal Functions for the Sobolev Inequality on Cartan-Hadamard Manifolds. - Semiconvexity of Viscosity Solutions to Fully Nonlinear Evolution Equations via Discrete Games. - An Interpolating Inequality for Solutions of Uniformly Elliptic Equations. - Asymptotic Behavior of Solutions for a Fourth Order Parabolic Equation with Gradient Nonlinearity via the Galerkin Method. - A Note on Radial Solutions to the Critical Lane-Emden Equation with a Variable Coefficient. - Remark on One Dimensional Semilinear DampedWave Equation in a CriticalWeighted L2-space.