Elliptic boundary value problems with Gaussian white noise loads

Elliptic Boundary-Value Problems

In the first part of this chapter we focus on the question of well-posedness of boundary-value problems for linear partial differential equations of elliptic type. The second part is devoted to the construction and the error analysis of finite difference schemes for these problems. It will be assumed throughout that the coefficients in the equation, the boundary data and the resulting solution ...

Sub - Elliptic Boundary Value Problems Forquasilinear Elliptic

Classical solvability and uniqueness in the HH older space C 2+ () is proved for the oblique derivative problem a ij (x)D ij u + b(x; u; Du) = 0 in ; @u=@`= '(x) on @ in the case when the vector eld`(x) = (` 1 (x); : : : ; ` n (x)) is tangential to the boundary @ at the points of some non-empty set S @; and the nonlinear term b(x; u; Du) grows quadratically with respect to the gradient Du. 0. I...

Nonlinear Elliptic Boundary Value Problems

It is the object of the present note to present a new nonlinear version of the orthogonal projection method for proving the existence of solutions of nonlinear elliptic boundary value problems. The key point in this method is the application of a new general theorem concerning the solvability of nonlinear functional equations in a reflexive Banach space involving operators which may not be cont...

Nonlocal Elliptic Boundary Value Problems

A White Noise Approach to Stochastic Neumann Boundary Value Problems

We illustrate the use of white noise analysis in the solution of stochastic partial diierential equations by solving explicitly the stochastic Neumann boundary value problem LU(x) ? c(x)U(x) = 0; x 2 D R d ; (x) rU(x) = ?W(x); x 2 @D where L is a uniformly elliptic linear partial diierential operator and W (x), x 2 R d , is d-parameter white noise. 1. Introduction Since the seminal book by Hida...