Compactness, interpolation inequalities for small Lebesgue-Sobolev spaces and applications期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Compactness, interpolation inequalities for small Lebesgue-Sobolev spaces and applications

Authors:	A. Fiorenza J. M. Rakotoson

Affiliation:	(1) Dipartimento di Costruzioni e Metodi Matematici in Architettura, Universitá di Napoli “Federico II”, via Monteoliveto, 3, I-80134 Napoli, Italy;(2) Istituto per le Applicazioni del Calcolo “Mauro Picone”, sezione di Napoli, Consiglio Nazionale delle Ricerche via Pietro Castellino, 111, I-80131 Napoli, Italy;(3) Département de Mathématiques UMR 6086, Université de Poitiers, Teleport 2 B.P. 30179, Boulevard Marie et Bierre Curie, 86962 Futuroscope Chasseneuil Cedex, France

Abstract:	We study some generalized small Lebesgue spaces and their associated Sobolev spaces. In particular, we prove that small Lebesgue-Sobolev spaces W^1,(p(Ω) are compactly embedded in $L^{frac{np}{n-p}}(O), p<n$ , p < n. As an application, we study variational problems involving critical exponents under multiple constraints. Mathematics Subject Classification (2000) 46E30, 46E35, 46B70, 26D07, 35J60.

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