Differential and Integral Equations
- Differential Integral Equations
- Volume 18, Number 11 (2005), 1201-1220.
Compactness and quasilinear problems with critical exponents
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.
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