Geometric properties for parabolic and elliptic PDE's

Chapter 1 Stability and Instability of Group Invariant Asymptotic Profiles for Fast Diffusion Equations

Chapter 2 A Family of Hardy-Rellich Type Inequalities Involving the L 2 -Norm of the Hessian Matrices

Chapter 3 Power Concavity for Solutions of Nonlinear Elliptic Problems in Convex Domains

Chapter 4 The Heart of a Convex Body

Chapter 6 Kato’s Inequality in the Half Space: An Alternative Proof and Relative Improvements

Chapter 7 Sharp Bounds for the p -Torsion of Convex Planar Domains

Chapter 8 Geometric Analysis of Fractional Phase Transition Interfaces

Chapter 9 Existence of Solutions to Some Classical Variational Problems

Chapter 10 Existence of Minimizers for Some Coupled Nonlinear Schrödinger Equations

Chapter 11 Decay Rate of L q Norms of Critical Schrödinger Heat Semigroups

Chapter 12 Hadamard Variation for Electromagnetic Frequencies

Chapter 13 Global Structure of the Solution Set for a Semilinear Elliptic Problem Related to the Liouville Equation on an Annulus

Chapter 14 A Priori Estimates and Comparison Principle for Some Nonlinear Elliptic Equations

Chapter 15 Existence and Uniqueness of the n -Dimensional Helfrich Flow

Chapter 16 Ground States for Elliptic Equations in $\pmb{\mathbb{R}}^{2}$ with Exponential Critical Growth

Chapter 17 Stationary Level Surfaces and Liouville-Type Theorems Characterizing Hyperplanes

Chapter 18 Nonexistence of Multi-bubble Solutions for a Higher Order Mean Field Equation on Convex Domains