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.
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Translated from Problemy Matematicheskogo Analiza, No. 38, December 2008, pp. 37–46.
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Ivochkina, N.M., Filimonenkova, N.V. Lemma about increase of approximate solutions to the Dirichlet problem for m-Hessian equations. J Math Sci 156, 606–616 (2009). https://doi.org/10.1007/s10958-009-9277-6
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DOI: https://doi.org/10.1007/s10958-009-9277-6