Large solutions to an anisotropic quasilinear elliptic problem
In this paper we consider existence, asymptotic behavior near the boundary and uniqueness of positive solutions to the problem, in a bounded domain Ω ⊂ ℝN × ℝM, together with the boundary condition u (x, y) = ∞ on ∂Ω. We prove that the necessary and sufficient condition for the existence of a soluti...
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todo:paper_03733114_v189_n4_p689_GarciaMelian2023-10-03T15:30:18Z Large solutions to an anisotropic quasilinear elliptic problem García-Melián, J. Rossi, J.D. de Lis, J.C.S. In this paper we consider existence, asymptotic behavior near the boundary and uniqueness of positive solutions to the problem, in a bounded domain Ω ⊂ ℝN × ℝM, together with the boundary condition u (x, y) = ∞ on ∂Ω. We prove that the necessary and sufficient condition for the existence of a solution, to this problem is r > max{p-1, q-1}. Assuming that r > q-1 ≥ p-1 > 0 we will show that the exponent q controls the blow-up rates near the boundary in the sense that all points of ∂Ω share the same profile, that depends on q and r but not on p, with the sole exception of the vertical points (where the exponent p plays a role). © 2010 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03733114_v189_n4_p689_GarciaMelian |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
In this paper we consider existence, asymptotic behavior near the boundary and uniqueness of positive solutions to the problem, in a bounded domain Ω ⊂ ℝN × ℝM, together with the boundary condition u (x, y) = ∞ on ∂Ω. We prove that the necessary and sufficient condition for the existence of a solution, to this problem is r > max{p-1, q-1}. Assuming that r > q-1 ≥ p-1 > 0 we will show that the exponent q controls the blow-up rates near the boundary in the sense that all points of ∂Ω share the same profile, that depends on q and r but not on p, with the sole exception of the vertical points (where the exponent p plays a role). © 2010 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag. |
| format |
JOUR |
| author |
García-Melián, J. Rossi, J.D. de Lis, J.C.S. |
| spellingShingle |
García-Melián, J. Rossi, J.D. de Lis, J.C.S. Large solutions to an anisotropic quasilinear elliptic problem |
| author_facet |
García-Melián, J. Rossi, J.D. de Lis, J.C.S. |
| author_sort |
García-Melián, J. |
| title |
Large solutions to an anisotropic quasilinear elliptic problem |
| title_short |
Large solutions to an anisotropic quasilinear elliptic problem |
| title_full |
Large solutions to an anisotropic quasilinear elliptic problem |
| title_fullStr |
Large solutions to an anisotropic quasilinear elliptic problem |
| title_full_unstemmed |
Large solutions to an anisotropic quasilinear elliptic problem |
| title_sort |
large solutions to an anisotropic quasilinear elliptic problem |
| url |
http://hdl.handle.net/20.500.12110/paper_03733114_v189_n4_p689_GarciaMelian |
| work_keys_str_mv |
AT garciamelianj largesolutionstoananisotropicquasilinearellipticproblem AT rossijd largesolutionstoananisotropicquasilinearellipticproblem AT delisjcs largesolutionstoananisotropicquasilinearellipticproblem |
| _version_ |
1807318610193940480 |