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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| Published in | Journal of Differential Equations Vol. 235; no. 2; pp. 376 - 396 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
15.04.2007
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0022-0396 1090-2732 |
| DOI | 10.1016/j.jde.2007.01.009 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Tersenov, Alkis S. Tersenov, Aris S. |
| Author_xml | – sequence: 1 givenname: Alkis S. surname: Tersenov fullname: Tersenov, Alkis S. email: tersenov@math.uoc.gr organization: University of Crete, Department of Mathematics, 71409 Heraklion-Crete, Greece – sequence: 2 givenname: Aris S. surname: Tersenov fullname: Tersenov, Aris S. email: aterseno@uop.gr organization: University of Peloponnese, Department of Computer Science and Technology, 22100 Tripoli, Greece |
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| Cites_doi | 10.1016/j.na.2004.02.030 10.1016/j.anihpc.2003.12.001 10.57262/ade/1355867831 10.1016/S0294-1449(16)30238-4 10.1017/S0308210500003085 10.1090/S0002-9904-1969-12175-0 10.1023/B:MATN.0000043484.27246.b3 10.1080/03605309808821412 |
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| Keywords | 35J25 Semilinear elliptic equations 35J70 35B45 A priori estimates Degenerate elliptic equations |
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| SubjectTerms | A priori estimates Degenerate elliptic equations Semilinear elliptic equations |
| Title | The problem of Dirichlet for anisotropic quasilinear degenerate elliptic equations |
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