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Mat. Zametki, 2004, Volume 76, Issue 4, Pages 592–603 (Mi mz134)  

This article is cited in 1 scientific paper (total in 1 paper)

Dirichlet Problem for a Class of Quasilinear Elliptic Equations

A. S. Tersenov


Abstract: In this paper, the Dirichlet problem for quasilinear elliptic equations is studied. New a priori estimates of the solution and its gradient are obtained. These estimates are derived without any assumptions on the smoothness of the coefficients and the right-hand side of the equation. Moreover, an arbitrary growth of the right-hand side with respect to the gradient of the solution is assumed. On the basis of the resulting estimates, existence theorems are proved.

DOI: https://doi.org/10.4213/mzm134

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English version:
Mathematical Notes, 2004, 76:4, 546–557

Bibliographic databases:

UDC: 517.95
Received: 28.08.2002

Citation: A. S. Tersenov, “Dirichlet Problem for a Class of Quasilinear Elliptic Equations”, Mat. Zametki, 76:4 (2004), 592–603; Math. Notes, 76:4 (2004), 546–557

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/mz/v76/i4/p592

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Tersenov, AS, “The problem of Dirichlet for anisotropic quasilinear degenerate elliptic equations”, Journal of Differential Equations, 235:2 (2007), 376  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  • Математические заметки Mathematical Notes
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