Entropy solutions of Dirichlet problem for a class of nonlinear elliptic high-order equations with L¹-data

Abstract

In this paper we study Dirichlet problem for nonlinear elliptic high-order equations with coefficients satisfying a strengthened ellipticity condition. A class of nonlinear high-order equations with such a condition on coefficients and data which are within usual theory of monotone operators [7] has been introduced in [9], where Holder continuity of generalized solutions of equations of that class has been established. Unlike [9] equations under consideration in the present paper have L¹-right-hand sides. Their solvability does not follow directly from results of the theory of monotone operators and on the whole it is a rather difficult problem.