Artículo
Manfredi, J.J.; Rossi, J.D.; Urbano, J.M. "Limits as p (x) → ∞ of p (x)-harmonic functions" (2010) Nonlinear Analysis, Theory, Methods and Applications. 72(1):309-315
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Abstract:
In this note we study the limit as p (x) → ∞ of solutions to - Δp (x) u = 0 in a domain Ω, with Dirichlet boundary conditions. Our approach consists in considering sequences of variable exponents converging uniformly to + ∞ and analyzing how the corresponding solutions of the problem converge and which equation is satisfied by the limit. © 2009 Elsevier Ltd. All rights reserved.
Registro:
| Documento: | Artículo |
| Título: | Limits as p (x) → ∞ of p (x)-harmonic functions |
| Autor: | Manfredi, J.J.; Rossi, J.D.; Urbano, J.M. |
| Filiación: | Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, United States Departamento de Matemática, FCEyN UBA, 1428 Buenos Aires, Argentina CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal |
| Palabras clave: | Infinity Laplacian; p (x)-Laplacian; Variable exponents; Viscosity solutions; Corresponding solutions; Dirichlet boundary condition; Harmonic function; Laplacians; P (x)-Laplacian; Viscosity solutions; Fourier series; Harmonic analysis; Viscosity; Laplace transforms |
| Año: | 2010 |
| Volumen: | 72 |
| Número: | 1 |
| Página de inicio: | 309 |
| Página de fin: | 315 |
| DOI: | http://dx.doi.org/10.1016/j.na.2009.06.054 |
| Título revista: | Nonlinear Analysis, Theory, Methods and Applications |
| Título revista abreviado: | Nonlinear Anal Theory Methods Appl |
| ISSN: | 0362546X |
| CODEN: | NOAND |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0362546X_v72_n1_p309_Manfredi |
Referencias:
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- Aronsson, G., Crandall, M.G., Juutinen, P., A tour of the theory of absolutely minimizing functions (2004) Bull. Amer. Math. Soc., 41, pp. 439-505
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- J.J. Manfredi, J.D. Rossi, J.M. Urbano, p (x)-Harmonic functions with unbounded exponent in a subdomain (submitted for publication). arXiv:0809.2731v3 [math.AP]; Lindqvist, P., Lukkari, T., A curious equation involving the ∞-Laplacian Preprint; Barles, G., Busca, J., Existence and comparison results for fully nonlinear degenerate elliptic equations without zeroth-order term (2001) Comm. Partial Differential Equations, 26, pp. 2323-2337
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Citas:
---------- APA ----------
Manfredi, J.J., Rossi, J.D. & Urbano, J.M. (2010) . Limits as p (x) → ∞ of p (x)-harmonic functions. Nonlinear Analysis, Theory, Methods and Applications, 72(1), 309-315.http://dx.doi.org/10.1016/j.na.2009.06.054
---------- CHICAGO ----------
Manfredi, J.J., Rossi, J.D., Urbano, J.M. "Limits as p (x) → ∞ of p (x)-harmonic functions" . Nonlinear Analysis, Theory, Methods and Applications 72, no. 1 (2010) : 309-315.http://dx.doi.org/10.1016/j.na.2009.06.054
---------- MLA ----------
Manfredi, J.J., Rossi, J.D., Urbano, J.M. "Limits as p (x) → ∞ of p (x)-harmonic functions" . Nonlinear Analysis, Theory, Methods and Applications, vol. 72, no. 1, 2010, pp. 309-315.http://dx.doi.org/10.1016/j.na.2009.06.054
---------- VANCOUVER ----------
Manfredi, J.J., Rossi, J.D., Urbano, J.M. Limits as p (x) → ∞ of p (x)-harmonic functions. Nonlinear Anal Theory Methods Appl. 2010;72(1):309-315.http://dx.doi.org/10.1016/j.na.2009.06.054
