Magnanini R., Sakaguchi S., Alvino A. (eds.) Geometric Properties for Parabolic and Elliptic PDE's

Springer, 2013. — 294 p. — (Springer INdAM Series 02). — ISBN: 978-88-470-2840-1.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.Stability and Instability of Group Invariant Asymptotic Profiles for Fast Diffusion Equations
A Family of Hardy-Rellich Type Inequalities Involving the L 2-Norm of the Hessian Matrices
Power Concavity for Solutions of Nonlinear Elliptic Problems in Convex Domains
The Heart of a Convex Body
A Viscosity Equation for Minimizers of a Class of Very Degenerate Elliptic Functionals
Kato’s Inequality in the Half Space: An Alternative Proof and Relative Improvements
Sharp Bounds for the p-Torsion of Convex Planar Domains
Geometric Analysis of Fractional Phase Transition Interfaces
Existence of Solutions to Some Classical Variational Problems
Existence of Minimizers for Some Coupled Nonlinear Schrödinger Equations
Decay Rate of L q Norms of Critical Schrödinger Heat Semigroups
Hadamard Variation for Electromagnetic Frequencies
Global Structure of the Solution Set for a Semilinear Elliptic Problem Related to the Liouville Equation on an Annulus
A Priori Estimates and Comparison Principle for Some Nonlinear Elliptic Equations
Existence and Uniqueness of the n-Dimensional Helfrich Flow
Ground States for Elliptic Equations in $\pmb{\mathbb{R}}^{2}$ with Exponential Critical Growth
Stationary Level Surfaces and Liouville-Type Theorems Characterizing Hyperplanes
Nonexistence of Multi-bubble Solutions for a Higher Order Mean Field Equation on Convex Domains