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RESEARCH PRODUCT

Anisotropic -Laplacian equations when goes to

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Abstract In this paper we prove a stability result for an anisotropic elliptic problem. More precisely, we consider the Dirichlet problem for an anisotropic equation, which is as the p -Laplacian equation with respect to a group of variables and as the q -Laplacian equation with respect to the other variables ( 1 p q ), with datum f belonging to a suitable Lebesgue space. For this problem, we study the behaviour of the solutions as p goes to 1 , showing that they converge to a function u , which is almost everywhere finite, regardless of the size of the datum f . Moreover, we prove that this u is the unique solution of a limit problem having the 1-Laplacian operator with respect to the first group of variables. Furthermore, the regularity of the solutions to the limit problem is studied and explicit examples are shown.