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.
Comparison results for nonlinear divergence structure elliptic PDE's
Marras M.;
2019-01-01
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.
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