Problems for p-Monge-Ampère equations

ANEDDA, CLAUDIA;CADEDDU, LUCIO;Porru, G.

2012-01-01

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Abstract

We consider the homogeneous Dirichlet problem for a class of equations which generalize the p-Laplace equations as well as the Monge- Amp`ere equations in a strictly convex domain Ω ⊂ Rn, n ≥ 2. In the sub-linear case, we study the comparison between quantities involving the solution to this boundary value problem and the corresponding quantities involving the (radial) solution of a problem in a ball having the same η1- mean radius as Ω. Next, we consider the eigenvalue problem for such a p-Monge-Amp`ere equation and study a comparison between its principal eigenvalue (eigenfunction) and the principal eigenvalue (eigenfunction) of the corresponding problem in a ball having the same η1-mean radius as Ω. Symmetrization techniques and comparison principles are the main tools used to get our results.