Nonlinear second order elliptic equations with Venttsel boundary conditions

Abstract

This thesis is concerned with second order elliptic equations with cenain second order boundary conditions which are called Venttsel boundary conditions. This sort of boundary condition originally came from probability theory. An example of such a boundary value problem of PDE also arises from a model in three dimensional water wave theory. Venttsel boundary conditions contain Dirichlet, Neumann, oblique and mixed boundary conditions as special cases, and from the probability point of view they are the most general admissible boundary conditions for second order elliptic operators.