). The function g(x,u)
satisfies suitable growth assumptions, but no sign hypothesis on it is assumed.
We prove that the rearrangement of u can be estimated by the solution of a
problem whose data are radially symmetric.
A Symmetrization Result for Nonlinear Elliptic Equations
Dipartimento di Matematica e Applicazioni “R.Caccioppoli” Università di Napoli “Federico II” Complesso Univ. Monte S. Angelo Via Cintia - 80126 Napoli — Italy | Dipartimento di Matematica e Applicazioni “R.Caccioppoli”
Università di Napoli “Federico II” Via Claudio, 21 - 80125 Napoli — Italy |
Received: February 21, 2003
Accepted:
September 30, 2003
We consider a solution u of the homogeneous Dirichlet problem for a class of
nonlinear elliptic equations in the form A(u) = g(x,u) + f, where the principal
term is a Leray-Lions operator defined on W01
,p
(). The function g(x,u)
satisfies suitable growth assumptions, but no sign hypothesis on it is assumed.
We prove that the rearrangement of u can be estimated by the solution of a
problem whose data are radially symmetric.
Key words: symmetrization, rearrangement, nonlinear elliptic PDE’s.
2000 Mathematics Subject Classification: 35J65, 35B45.