### Dirichlet problem in a ball for Laplace’s equation with Laplacian with respect to a measure

#### Abstract

We propose a general solution construction framework for the Dirichlet problem in a ball in 2- and 3-dimensional spaces in the case of densities, that are invariant to orthogonal transforms. Using this framework we find explicit solutions for several important and rich families of densities, with the Gaussian density among them.

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