Geometric Properties for Parabolic and Elliptic PDE's [Hardcover]

The study of qualitative aspects of PDE's has always attracted much attention from the early beginnings. More recently, once basic issues about PDE's, such as existence, uniqueness and stability of solutions, have been understood quite well, research on topological and/or geometric properties of their solutions has become more intense. The study of these issues is attracting the interest of an increasing number of researchers and is now a broad and well-established research area, with contributions that often come from experts from disparate areas of mathematics, such as differential and convex geometry, functional analysis, calculus of variations, mathematical physics, to name a few.

This volume collects a selection of original results and informative surveys by a group of international specialists in the field, analyzes new trends and techniques and aims at promoting scientific collaboration and stimulating future developments and perspectives in this very active area of research.

This inclusive study of projective geometry covers analytic and synthetic methods, takes in linear, quadratic, cubic and quartic figures in various dimensions, and deals at length with refinements of basic theories, including those of Pappus and Desargues.

Goro Akagi, Stability and instability of group invariant asymptotic profiles for fast diffusion equations.- Elvise Berchio, A family of Hardy-Rellich type inequalities involving the L2-norm of the Hessian matrices.- Massimiliano Bianchini and Paolo Salani, Power concavity for solutions of nonlinear elliptic problems in convex domains.- Lorenzo Brasco and Rolando Magnanini, The heart of a convex set.- Giulio Ciraolo, A viscosity equation for minimizers of a class of very degenerate elliptic functionals.- Adele Ferone, Kato's inequality in the half space: an alternative proof and relative improvements.- Ilaria Fragal?, Filippo Gazzola and Jimmy Lamboley, Sharp bounds for thelsÚ