PARTIAL REGULARITY OF SOLUTIONS TO MODEL VENTTSEL PROBLEM FOR QUASILINEAR ELLIPTIC SYSTEMS OF EQUATIONS WITH QUADRATIC NON-LINEARITY RELATIVE TO THE GRADIENT

摘要

We consider the model Venttsel boundary value problem for quasilinear elliptic systems of equations with the Venttsel boundary condition. Using the method of A-harmonic approximation, we prove the partial regularity of a weak solution to the problem in a neighborhood of the plane part of the boundary. Preliminarily, we describe a condition guaranteeing the local Holder continuity of the solution along this boundary part. We prove the Holder continuity of the solution in a neighborhood of a boundary point and describe a possible singular set of solutions. Bibliography: 10 titles.