Open Access
2005 Compactness and quasilinear problems with critical exponents
A. El Hamidi, J. M. Rakotoson
Differential Integral Equations 18(11): 1201-1220 (2005). DOI: 10.57262/die/1356059738


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.


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A. El Hamidi. J. M. Rakotoson. "Compactness and quasilinear problems with critical exponents." Differential Integral Equations 18 (11) 1201 - 1220, 2005.


Published: 2005
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35113
MathSciNet: MR2174817
Digital Object Identifier: 10.57262/die/1356059738

Primary: 35J20
Secondary: 35B33 , 35J60 , 35J85

Rights: Copyright © 2005 Khayyam Publishing, Inc.

Vol.18 • No. 11 • 2005
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