Geometric Properties for Parabolic and Elliptic PDE's: GPPEPDEs, Palinuro, Italy, May 2015 (Springer Proceedings in Mathematics & Statistics, 176)

This book collects recent research papers by respected specialists in the field. It presents advances in the field of geometric properties for parabolic and elliptic partial differential equations, an area that has always attracted great attention. It settles the basic issues (existence, uniqueness, stability and regularity of solutions of initial/boundary value problems) before focusing on the topological and/or geometric aspects. These topics interact with many other areas of research and rely on a wide range of mathematical tools and techniques, both analytic and geometric. The Italian and Japanese mathematical schools have a long history of research on PDEs and have numerous active groups collaborating in the study of the geometric properties of their solutions. Front Matter....Pages i-viii Estimates for Solutions to Anisotropic Elliptic Equations with Zero Order Term....Pages 1-15 A Topological Approach to Non-Archimedean Mathematics....Pages 17-40 A Note on an Overdetermined Problem for the Capacitary Potential....Pages 41-48 A Note on Some Poincaré Inequalities on Convex Sets by Optimal Transport Methods....Pages 49-63 Analyticity and Criticality Results for the Eigenvalues of the Biharmonic Operator....Pages 65-85 A Remark on an Overdetermined Problem in Riemannian Geometry....Pages 87-96 A Note on the Scale Invariant Structure of Critical Hardy Inequalities....Pages 97-120 Stability Analysis of Delaunay Surfaces as Steady States for the Surface Diffusion Equation....Pages 121-148 Littlewood’s Fourth Principle....Pages 149-158 The Phragmèn-Lindelöf Theorem for a Fully Nonlinear Elliptic Problem with a Dynamical Boundary Condition....Pages 159-171 Entire Solutions to Generalized Parabolic k-Hessian Equations....Pages 173-190 Dynamical Aspects of a Hybrid System Describing Intermittent Androgen Suppression Therapy of Prostate Cancer....Pages 191-230 Symmetry Problems on Stationary Isothermic Surfaces in Euclidean Spaces....Pages 231-239 Improved Rellich Type Inequalities in \({\mathbb {R}}^{N}\) ....Pages 241-255 Solvability of a Semilinear Parabolic Equation with Measures as Initial Data....Pages 257-276 Singular Solutions of the Scalar Field Equation with a Critical Exponent....Pages 277-288