Comparison results for nonlinear divergence structure elliptic PDE's

Liu Y.

;Marras M.;Porru G.

2019-01-01

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Abstract

First we prove a comparison result for a nonlinear divergence structure elliptic partial differential equation. Next we find an estimate of the solution of a boundary value problem in a domain Omega in terms of the solution of a related symmetric boundary value problem in a ball B having the same measure as Omega. For p Laplace equations, the corresponding result is due to Giorgio Talenti. In a special (radial) case we also prove a reverse comparison result.