On γ-weak solutions of elliptic equations

Abstract

We build on the "alternative" approach to the Dirichlet problem in weighted Sobolev spaces (cf.A. Kufner & J. Rakosnik, [11]) to formulate sufficient conditions for interior regularity of γ-weak solutions of the Dirichlet problem for second order elliptic PDEs with Lipschitz coefficients. Next,we prove a maximum principle (for γ-weak subsolutions). Last, we generalize (from power type weights to a larger class of weights) a truce theorem by J. Necas, [14].