The problem of Dirichlet for anisotropic quasilinear degenerate elliptic equations

We consider the Dirichlet problem for a class of anisotropic degenerate elliptic equations. New a priori estimates for solutions and for the gradient of solutions are established. Based on these estimates sufficient conditions guaranteeing the solvability of the problem are formulated. The results a...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 235; no. 2; pp. 376 - 396
Main Authors Tersenov, Alkis S., Tersenov, Aris S.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.04.2007
Subjects
A priori estimates
Degenerate elliptic equations
Semilinear elliptic equations
35J25
Semilinear elliptic equations
35J70
35B45
A priori estimates
Degenerate elliptic equations
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ISSN0022-0396
1090-2732
DOI10.1016/j.jde.2007.01.009

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Summary:We consider the Dirichlet problem for a class of anisotropic degenerate elliptic equations. New a priori estimates for solutions and for the gradient of solutions are established. Based on these estimates sufficient conditions guaranteeing the solvability of the problem are formulated. The results are new even in the semilinear case when the principal part is the Laplace operator.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2007.01.009