Journal of Mathematical Sciences

, Volume 166, Issue 3, pp 338–356 | Cite as

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

  • N. V. Filimonenkova

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.


Weak Solution Dirichlet Problem Barrier Function Convex Surface Morrey Space 
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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.St. Petersburg State University of Architecture and Civil Engineering 4St. PetersburgRussia

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