Fundamental Solutions and Asymptotic Behaviour for the p-Laplacian Equation

• Autores: Shoshana Kamin, Juan Luis Vázquez
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 4, Nº 2, 1988, págs. 339-354
• Idioma: inglés
• Títulos paralelos:
  • Soluciones fundamentales y comportamiento asintótico para la ecuación p-laplaciana.
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• Resumen

  • We establish the uniqueness of fundamental solutions to the p-Laplacian equation ut = div (|Du|p-2 Du), p > 2, defined for x Î RN, 0 < t < T. We derive from this result the asymptotic behavoir of nonnegative solutions with finite mass, i.e., such that u(*,t) Î L1(RN). Our methods also apply to the porous medium equation ut = ?(um), m > 1, giving new and simpler proofs of known results. We finally introduce yet another method of proving asymptotic results based on the idea of asymptotic radial symmetry. This method can be useful in dealing with more general equations.