Bocea, Marian; Mihăilescu, Ilescu A Caffarelli-Kohn-Nirenberg inequality in Orlicz-Sobolev spaces and applications. (English) Zbl 1251.35028 Appl. Anal. 91, No. 9, 1649-1659 (2012). Summary: A generalization of the classical Caffarelli-Kohn-Nirenberg inequality is obtained in the setting of Orlicz-Sobolev spaces. As applications, we prove a compact embedding result, and we establish the existence of weak solutions of the Dirichlet problem for a nonhomogeneous and degenerate/singular elliptic PDE. Cited in 2 Documents MSC: 35J70 Degenerate elliptic equations 35D30 Weak solutions to PDEs 35J75 Singular elliptic equations 49J45 Methods involving semicontinuity and convergence; relaxation Keywords:Caffarelli-Kohn-Nirenberg inequality; critical point; degenerate elliptic equations; Orlicz spaces PDFBibTeX XMLCite \textit{M. Bocea} and \textit{I. Mihăilescu}, Appl. Anal. 91, No. 9, 1649--1659 (2012; Zbl 1251.35028) Full Text: DOI References: [1] Caffarelli L, Compos. Math. 53 pp 259– (1984) [2] DOI: 10.1007/s005260050130 · Zbl 0929.35045 · doi:10.1007/s005260050130 [3] DOI: 10.1007/s000300050004 · Zbl 0960.35039 · doi:10.1007/s000300050004 [4] DOI: 10.1002/1097-0312(200102)54:2<229::AID-CPA4>3.0.CO;2-I · Zbl 1072.35506 · doi:10.1002/1097-0312(200102)54:2<229::AID-CPA4>3.0.CO;2-I [5] DOI: 10.1006/jdeq.1999.3699 · Zbl 0954.35074 · doi:10.1006/jdeq.1999.3699 [6] DOI: 10.3934/dcds.2006.15.447 · Zbl 1163.35023 · doi:10.3934/dcds.2006.15.447 [7] DOI: 10.1007/s10231-004-0143-3 · Zbl 1115.35050 · doi:10.1007/s10231-004-0143-3 [8] Gilbarg D, Elliptic Partial Differential Equations of Second Order (1998) [9] Adams R, Sobolev Spaces (1975) [10] Adams DR, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 314 (1996) [11] DOI: 10.1007/s00009-004-0014-6 · Zbl 1167.35352 · doi:10.1007/s00009-004-0014-6 [12] Willem M, Analyse Fonctionnelle Elémentaire (2003) [13] Rao MM, Theory of Orlicz Spaces (1991) [14] DOI: 10.1007/s005260050002 · doi:10.1007/s005260050002 [15] DOI: 10.1007/s000300050073 · Zbl 0936.35067 · doi:10.1007/s000300050073 [16] DOI: 10.1090/S0002-9947-1974-0342854-2 · doi:10.1090/S0002-9947-1974-0342854-2 [17] DOI: 10.5802/aif.2407 · Zbl 1186.35065 · doi:10.5802/aif.2407 [18] DOI: 10.1619/fesi.49.235 · Zbl 1387.35405 · doi:10.1619/fesi.49.235 [19] DOI: 10.1142/S0219530508001067 · Zbl 1159.35051 · doi:10.1142/S0219530508001067 [20] Struwe M, Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems (1996) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.