Differential and Integral Equations

Compactness and quasilinear problems with critical exponents

A. El Hamidi and J. M. Rakotoson

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


A compactness result is revised in order to prove the pointwise convergence of the gradients of a sequence of solutions to a general quasilinear inequality (anisotropic or not, degenerate or not) and for an arbitrary open set. Combining this result with the well-known Brézis-Lieb lemma, we derive simple proofs of Palais-Smale properties in many optimization problems especially on unbounded domains.

Article information

Differential Integral Equations, Volume 18, Number 11 (2005), 1201-1220.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J20: Variational methods for second-order elliptic equations
Secondary: 35B33: Critical exponents 35J60: Nonlinear elliptic equations 35J85


El Hamidi, A.; Rakotoson, J. M. Compactness and quasilinear problems with critical exponents. Differential Integral Equations 18 (2005), no. 11, 1201--1220. https://projecteuclid.org/euclid.die/1356059738

Export citation