Comparison results for nonlinear divergence structure elliptic PDE’s

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 Ω in terms of the solution of a related symmetric boundary value problem in a ball B having the same measure as Ω. For p-Laplace equations, the corresponding result is due to Giorgio Talenti. In a special (radial) case we also prove a reverse comparison result.

Keywords

• quasi-linear equations
• symmetrization
• comparison results
• 35b51
• 35j62
• 49k20
• 49k30