Differential and Integral Equations

Compactness and quasilinear problems with critical exponents

A. El Hamidi and J. M. Rakotoson

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Abstract

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

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

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356059738

Mathematical Reviews number (MathSciNet)
MR2174817

Zentralblatt MATH identifier
1212.35113

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

Citation

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


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