On local compactness in quasilinear elliptic problems
Analysis of PDEs
2008-12-05 v1
Abstract
One of the major difficulties in nonlinear elliptic problems involving critical nonlinearities is the compactness of Palais-Smale sequences. In their celebrated work \cite{BN}, Br\'ezis and Nirenberg introduced the notion of critical level for these sequences in the case of a critical perturbation of the Laplacian homogeneous eigenvalue problem. In this paper, we give a natural and general formula of the critical level for a large class of nonlinear elliptic critical problems. The sharpness of our formula is established by the construction of suitable Palais-Smale sequences which are not relatively compact.
Cite
@article{arxiv.0812.0927,
title = {On local compactness in quasilinear elliptic problems},
author = {Khalid Adriouch and Abdallah El Hamidi},
journal= {arXiv preprint arXiv:0812.0927},
year = {2008}
}