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Abstract:

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.

Registro:

Documento: Artículo
Título:Large solutions to an anisotropic quasilinear elliptic problem
Autor:García-Melián, J.; Rossi, J.D.; de Lis, J.C.S.
Filiación:Departamento de Análisis Matemático, Universidad de La Laguna, C/. Astrofísico Francisco Sánchez s/n, 38271 La Laguna, Spain
Departamento de Matemática, FCEyN UBA, Universidad de Buenos Aires, Pab 1, (1428), Buenos Aires, Argentina
Instituto Universitario de Estudios Avanzados (IUdEA) en Física Atomica, Molecular y Fotonica, Facultad de Física, Universidad de La Laguna, C/. Astrofísico Francisco Sánchez s/n, 38203 La Laguna, Spain
Año:2010
Volumen:189
Número:4
Página de inicio:689
Página de fin:712
DOI: http://dx.doi.org/10.1007/s10231-010-0132-7
Título revista:Annali di Matematica Pura ed Applicata
Título revista abreviado:Ann. Mat. Pura Appl.
ISSN:03733114
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03733114_v189_n4_p689_GarciaMelian

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Citas:

---------- APA ----------
García-Melián, J., Rossi, J.D. & de Lis, J.C.S. (2010) . Large solutions to an anisotropic quasilinear elliptic problem. Annali di Matematica Pura ed Applicata, 189(4), 689-712.
http://dx.doi.org/10.1007/s10231-010-0132-7
---------- CHICAGO ----------
García-Melián, J., Rossi, J.D., de Lis, J.C.S. "Large solutions to an anisotropic quasilinear elliptic problem" . Annali di Matematica Pura ed Applicata 189, no. 4 (2010) : 689-712.
http://dx.doi.org/10.1007/s10231-010-0132-7
---------- MLA ----------
García-Melián, J., Rossi, J.D., de Lis, J.C.S. "Large solutions to an anisotropic quasilinear elliptic problem" . Annali di Matematica Pura ed Applicata, vol. 189, no. 4, 2010, pp. 689-712.
http://dx.doi.org/10.1007/s10231-010-0132-7
---------- VANCOUVER ----------
García-Melián, J., Rossi, J.D., de Lis, J.C.S. Large solutions to an anisotropic quasilinear elliptic problem. Ann. Mat. Pura Appl. 2010;189(4):689-712.
http://dx.doi.org/10.1007/s10231-010-0132-7