Abstract:
In this work we consider the behaviour for large values of p of the unique positive weak solution u p to Δ p u = u q in Ω, u = +∞ on partial Ω, where q > p - 1. We take q = q(p) and analyze the limit of u p as p → ∞. We find that when q(p)/p → Q the behaviour strongly depends on Q. If 1 < Q < ∞ then solutions converge uniformly in compacts to a viscosity solution of max{-Δ{u}, -|∇ u| +uQ \\} = 0 with u = +∞ on Ω. If Q = 1 then solutions go to ∞ in the whole Ω and when Q = ∞ solutions converge to 1 uniformly in compact subsets of Ω, hence the boundary blow-up is lost in the limit. © 2007 Springer-Verlag.
Registro:
Documento: |
Artículo
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Título: | Large solutions to the p-Laplacian for large p |
Autor: | García-Melián, J.; Rossi, J.D.; De Lis, J.C.S. |
Filiación: | Dpto. de Análisis Matemático, Universidad de la Laguna, C/. Astrofísico Francisco Sánchez s/n, 38271 La Laguna, Spain Instituto de Matemáticas y Física Fundamental, Consejo Superior de Investigaciones Científicas, C/. Serrano 123, Madrid, Spain Departamento de Matemática, FCEyN UBA (1428), Buenos Aires, Argentina
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Año: | 2008
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Volumen: | 31
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Número: | 2
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Página de inicio: | 187
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Página de fin: | 204
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DOI: |
http://dx.doi.org/10.1007/s00526-007-0109-6 |
Título revista: | Calculus of Variations and Partial Differential Equations
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Título revista abreviado: | Calc. Var. Partial Differ. Equ.
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ISSN: | 09442669
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09442669_v31_n2_p187_GarciaMelian |
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Citas:
---------- APA ----------
García-Melián, J., Rossi, J.D. & De Lis, J.C.S.
(2008)
. Large solutions to the p-Laplacian for large p. Calculus of Variations and Partial Differential Equations, 31(2), 187-204.
http://dx.doi.org/10.1007/s00526-007-0109-6---------- CHICAGO ----------
García-Melián, J., Rossi, J.D., De Lis, J.C.S.
"Large solutions to the p-Laplacian for large p"
. Calculus of Variations and Partial Differential Equations 31, no. 2
(2008) : 187-204.
http://dx.doi.org/10.1007/s00526-007-0109-6---------- MLA ----------
García-Melián, J., Rossi, J.D., De Lis, J.C.S.
"Large solutions to the p-Laplacian for large p"
. Calculus of Variations and Partial Differential Equations, vol. 31, no. 2, 2008, pp. 187-204.
http://dx.doi.org/10.1007/s00526-007-0109-6---------- VANCOUVER ----------
García-Melián, J., Rossi, J.D., De Lis, J.C.S. Large solutions to the p-Laplacian for large p. Calc. Var. Partial Differ. Equ. 2008;31(2):187-204.
http://dx.doi.org/10.1007/s00526-007-0109-6