On Some Quasilinear Critical Problems

de Valeriola, Sébastien;Willem, Michel
(2009) Advanced Nonlinear Studies — Vol. 9, n° 4, p. 825-836 (2009)

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In this paper we prove the almost everywhere convergence of the gradient of Palais-Smale sequences, allowing us to apply the Brezis-Lieb lemma. This leads us to show that infima are attained, and thus to prove the existence of optimal solutions for some critical problems. Our method does not use the concentration-compactness principle.
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de Valeriola, S., & Willem, M. (2009). On Some Quasilinear Critical Problems. Advanced Nonlinear Studies, 9(4), 825-836. https://hdl.handle.net/2078.5/47034 (Original work published 2009)