ESTIMATE OF THE HOELDER CONSTANT FOR SOLUTIONS TO m-HESSIAN EQUATIONS

摘要

An a priori estimate for the Holder constant with exponent 0 < α < 1 is obtained for smooth solutions to m-Hessian equations in a closed domain with (m - l)-convex boundary of class C~2. The Holder constant depends on the L~p -norm, p > [n(n + l)]/2, of the right-hand side of the equation, and the estimate remains valid for approximate solutions.