Anisotropic nonlinear Neumann problems

Entropy Solutions for Nonlinear Elliptic Anisotropic Homogeneous Neumann Problem

Gradient-finite Element Method for Nonlinear Neumann Problems

We consider the numerical solution of quasilinear elliptic Neumann problems. The basic difficulty is the non-injectivity of the operator, which can be overcome by suitable factorization. We extend the gradient-finite element method (GFEM), introduced earlier by the authors for Dirichlet problems, to the Neumann problem. The algorithm is constructed and its convergence is proved.

Generalized BSDEs and nonlinear Neumann boundary value problems

We study a new class of backward stochastic di€erential equations, which involves the integral with respect to a continuous increasing process. This allows us to give a probabilistic formula for solutions of semilinear partial di€erential equations with Neumann boundary condition, where the boundary condition itself is nonlinear. We consider both parabolic and elliptic equations.

A Stability Result for Nonlinear Neumann Problems under Boundary Variations

In this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology. More precisely, for every bounded open subset Ω of R, we consider the problem

Conjugate Points Revisited and Neumann-Neumann Problems

The theory of conjugate points in the calculus of variations is reconsidered with a perspective emphasizing the connection to finite-dimensional optimization. The object of central importance is the spectrum of the second-variation operator, analogous to the eigenvalues of the Hessian matrix in finite dimensions. With a few basic properties of this spectrum, one can gain a new perspective on th...