Lemma About Increaseof Approximate Solutions To the Dirichlet Problem For M-hessian Equations

摘要

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 right-hand 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.