Lemma about increase of approximate solutions to the Dirichlet problem for <Emphasis Type="Italic">m</Emphasis>-Hessian equations

We prove an assertion about the increase of a solution, weak in the sense of Trudinger, to the Dirichlet problem for m-Hessian equations with the righthand side in L ^q , q > n(n + 1)/(2m). We estimate the ratio between the increment of the solution along the normal and the distance to the boundary of a domain. This assertion is also proved for some class of degenerate linear elliptic equations of second order. Bibliography: 7 titles. Translated from Problemy Matematicheskogo Analiza, No. 38, December 2008, pp. 37–46.