We introduce Monte Carlo methods to compute the solution of elliptic equations with pure Neumann boundary conditions. We first prove that the solution obtained by the stochastic representation has a zero mean value with respect to the invariant measure of the stochastic process associated to the equation. Pointwise approximations are computed by means of standard and new simulation schemes espe...

In this paper we are going to show the existence of a nontrivial solution to the following model problem,

This paper concerns a priori second order derivative estimates of solutions the Neumann problem for Monge-Amp\`ere type equations in bounded domains n dimensional Euclidean space. We first establish double normal estimate on boundary under an appropriate notion domain convexity. Then, assuming barrier condition linearized operator, we provide complete proof global elliptic solutions, as previou...

the bem is applied to the solution of the torsion problem of non-homogeneous anisotropic non-circular prismatic bars. the problem is formulated in terms of the warping function. this formulation leads to a second order partial differential equation with variable coefficients, subjected to a generalized neumann type boundary condition. the problem is solved using the analog equation method (aem)...