# Optimization in Problems Involving the P-laplacian

• MONICA MARRAS
• Published 2010

#### Abstract

Weminimize the energy integral R Ω |∇u| p dx, where g is a bounded positive function that varies in a class of rearrangements, p > 1, and u is a solution of −∆pu = g in Ω u = 0 on ∂Ω . Also we maximize the first eigenvalue λ = λg , where −∆pu = λgup−1 in Ω . For both problems, we prove existence, uniqueness, and representation of the optimizers.

### Cite this paper

@inproceedings{MARRAS2010OptimizationIP, title={Optimization in Problems Involving the P-laplacian}, author={MONICA MARRAS}, year={2010} }