Fundamental Solutions and Asymptotic Behaviour for the $p$-Laplacian Equation
Shoshana Kamin, Juan Luis Vázquez · Revista Matemática Iberoamericana · 1988
We establish the uniqueness of fundamental solutions to the p -Laplacian equation \mathrm {(PLE)} \; u_t = \mathrm {div} (|Du|^{p-2}Du), \; p > 2, defined for x \in \mathbb R^N , 0 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.