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Fundamental solutions and asymptotic behaviour for the p-Laplacian equation.

Soshana Kamin; Juan Luis Vázquez — 1988

Revista Matemática Iberoamericana

We establish the uniqueness of fundamental solutions to the p-Laplacian equation u_t = div (|Du|^p-2 Du), p > 2, defined for x ∈ R^N, 0 < t < T. We derive from this result the asymptotic behavoir of nonnegative solutions with finite mass, i.e., such that u(*,t) ∈ L¹(R^N). Our methods also apply to the porous medium equation u_t...

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