Anisotropic -Laplacian equations when goes to

✍ Scribed by A. Mercaldo; J.D. Rossi; S. Segura de León; C. Trombetti

• Book ID: 103850565
• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 422 KB
• Volume: 73
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2010.07.030

✦ Synopsis

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.