Giovanni Pisante

A Quantitative Second Order Minimality Criterion for Cavities in Elastic Bodies

We consider a functional which models an elastic body with a cavity. We show that if a critical point has positive second variation, then it is a strict local minimizer. We also provide a quantitative estimate.

An isoperimetric inequality for a nonlinear eigenvalue problem

Abstract We prove an isoperimetric inequality of the Rayleigh–Faber–Krahn type for a nonlinear generalization of the first twisted Dirichlet eigenvalue, defined by λ p , q ( Ω ) = inf { ‖ ∇ v ‖ L p ( Ω ) ‖ v ‖ L q ( Ω ) , v ≠ 0 , v ∈ W 0 1 , p ( Ω ) , ∫ Ω | v | q − 2 v d x = 0 } . More precisely, we show that the minimizer among sets of given volume is the union of two equal balls.

Sufficient conditions for the existence of viscosity solutions for nonconvex Hamiltonians

We study a sufficient geometric condition for the existence of a

On representation of boundary integrals involving the mean curvature for mean-convex domains

W^{1,\infty}(\Omega)

A SELECTION CRITERION OF SOLUTIONS TO A SYSTEM OF EIKONAL EQUATIONS

viscosity solution of the Hamilton--Jacobi equation

Sign-changing two-peak solutions for an elliptic free boundary problem related to confined plasmas

\left\{ \begin{array}{@{}r@{\;}c@{\;}lcc} F(Du) & = & 0 & \mbox{in} & \Omega, \\[2pt] u & = & \varphi & \mbox{on} & \partial\Omega, \end{array} \right.

The Semigeostrophic Equations Discretized in Reference and Dual Variables

where

Minimality via second variation for microphase separation of diblock copolymer melts

\Omega \subset {\mathbb R}^n