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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2010
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03733114_v189_n4_p689_GarciaMelian http://hdl.handle.net/20.500.12110/paper_03733114_v189_n4_p689_GarciaMelian |
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paper:paper_03733114_v189_n4_p689_GarciaMelian2023-06-08T15:37:54Z Large solutions to an anisotropic quasilinear elliptic problem Rossi, Julio Daniel 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. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03733114_v189_n4_p689_GarciaMelian http://hdl.handle.net/20.500.12110/paper_03733114_v189_n4_p689_GarciaMelian |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
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. |
| author |
Rossi, Julio Daniel |
| spellingShingle |
Rossi, Julio Daniel Large solutions to an anisotropic quasilinear elliptic problem |
| author_facet |
Rossi, Julio Daniel |
| author_sort |
Rossi, Julio Daniel |
| 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 |
| publishDate |
2010 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03733114_v189_n4_p689_GarciaMelian http://hdl.handle.net/20.500.12110/paper_03733114_v189_n4_p689_GarciaMelian |
| work_keys_str_mv |
AT rossijuliodaniel largesolutionstoananisotropicquasilinearellipticproblem |
| _version_ |
1768542990793441280 |