They present mathematical formulations of boundary integral equations for several of the most important linear elliptic boundary value problems, discuss their computational algorithms and the accuracy of their solutions, illustrate the numerical solutions, and show some applications.

Existence and uniqueness for a class of quasilinear elliptic boundary value problems.

1965, Lectures on Elliptic Boundary Value Problems, Van Nostrand Mathenmatical Studies 2, Princeton, NJ.

DAUGE, Elliptic Boundary Value Problems on Corner Domains, Lecture Notes in Mathematics 1341, Springer, Berlin-Heidelberg, 1988.

By regularity theory for elliptic boundary value problems u is a solution to (2) if and only if u is a critical point of the action functional J.

Some elementary generalizations of linear elliptic boundary value problems.

The WOPSIP method can also be applied to elliptic boundary value problems with variable coefficients that are Lipschitz continuous.

Keywords: Elliptic boundary value problems, multiple solutions, finite difference method.