Elliptic partial differential equations (PDEs) are a central pillar in the mathematical description of steady-state phenomena across physics, engineering, and applied sciences.

In this paper, we prove that there exists a unique solution to the Dirichlet boundary value problem for a general class of semilinear second order elliptic partial differential equations. Our approach ...

American Journal of Mathematics, Vol. 135, No. 6 (December 2013), pp. 1699-1726 (28 pages) We consider some elliptic pde's with Dirichlet and Neumann data prescribed on some portion of the boundary of ...