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Analysis of the behavior of a weak solution to m-Hessian equations near the boundary of a domain

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We consider the Dirichlet problem for the m-Hessian equations F m [u] = f in a domain Ω and analyze the behavior of approximate solutions at the boundary of Ω. We show that the growth rate for weak solutions towards to the boundary locally depends on the summability exponent of f or on the fact whether f belongs to a certain Morrey type space near the boundary. The result obtained can be used for estimating the Hölder constant for weak solutions in the closed domain. Bibliography: 11 titles.

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  1. St. Petersburg State University of Architecture and Civil Engineering 4, 2-nd Krasnoarmeiskaya Str., St. Petersburg, 190005, Russia

    N. V. Filimonenkova

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  1. N. V. Filimonenkova
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Correspondence to N. V. Filimonenkova.

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Translated from Problems in Mathematical Analysis 45, February 2010, pp. 103–118.

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Filimonenkova, N.V. Analysis of the behavior of a weak solution to m-Hessian equations near the boundary of a domain. J Math Sci 166, 338–356 (2010). https://doi.org/10.1007/s10958-010-9871-7

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  • DOI: https://doi.org/10.1007/s10958-010-9871-7

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