BOUNDEDLY NONHOMOGENEOUS ELLIPTIC AND PARABOLIC EQUATIONS IN A DOMAIN

Abstract

In this paper the Dirichlet problem is studied for equations of the form and also the first boundary value problem for equations of the form , where and are positive homogeneous functions of the first degree in , convex upwards in , that satisfy a uniform strict ellipticity condition. Under certain smoothness conditions on and when the second derivatives of with respect to are bounded above, the solvability of these problems in smooth domains is proved. In the course of the proof, a priori estimates in on the boundary are constructed, and convexity and restrictions on the second derivatives of are not used in the derivation. Bibliography: 13 titles.