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In this paper we consider PDE's problems involving the anisotropic Laplacianoperator, with Robin boundary conditions. By means of Talenti techniques,widely used in the last decades, we prove a comparison result between thesolutions of the above-mentioned problems and the solutions of the symmetrizedones. As a consequence of these results, a Bossel-Daners type inequality can beshown in dimension 2.

Comparison results for the solutions to the anisotropic Laplacian with Robin boundary conditions