THE INTEGRAL METHOD OF BARRIER FUNCTIONS AND THE DIRICHLET PROBLEM FOR EQUATIONS WITH OPERATORS OF MONGE-AMPÈRE TYPE

Abstract

A priori boundedness of the solution of the Dirichlet problem is proved for the equation , where is the sum of all principal minors of order in the Hessian . The boundedness in question is relative to the -norm and is demonstrated by combining the methods of integral inequalities and barrier functions. Bibliography: 7 titles.