Positive solutions for singular elliptic equations with critical Hardy-Sobolev exponent
نویسندگان
چکیده
منابع مشابه
Multiplicity of Solutions for Singular Semilinear Elliptic Equations with Critical Hardy-sobolev Exponents
where Ω ⊂ R(N ≥ 4) is an open bounded domain with smooth boundary, β > 0, 0 ∈ Ω, 0 ≤ s < 2, 2∗(s) := 2(N − s) N − 2 is the critical Hardy-Sobolev exponent and, when s = 0, 2∗(0) = 2N N − 2 is the critical Sobolev exponent, 0 ≤ μ < μ := (N − 2) 4 . In [1] A. Ferrero and F. Gazzola investigated the existence of nontrivial solutions for problem (1.1) with β = 1, s = 0. In [2] D. S. Kang and S. J. ...
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‖u‖ L pN N−p (RN ) ≤ C(N, p)‖u‖D1,p(RN ). Thus we use D loc(R N ) to denote those functions u which satisfy, on all compact subsets K of R , u ∈ L 2N N−2 (K) and ∇u ∈ L2(K). It is the same asH1 loc(R ), another standard notation which denotes the set of functions u satisfying u,∇u ∈ L2(K) for all compact subsets K of R . A D loc(R N ) solution of (1.1) is in L∞loc. This can be proved by argumen...
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and Applied Analysis 3 The following Hardy-Sobolev inequality is due to Caffarelli et al. 12 , which is called Caffarelli-Kohn-Nirenberg inequality. There exist constants S1, S2 > 0 such that (∫ RN |x|−bp |u|pdx )p/p∗ ≤ S1 ∫ RN |x|−ap|∇u|pdx, ∀u ∈ C∞ 0 ( R N ) , 1.8 ∫ RN |x|− a 1 |u|dx ≤ S2 ∫ RN |x|−ap|∇u|pdx, ∀u ∈ C∞ 0 ( R N ) , 1.9 where p∗ Np/ N − pd is called the Sobolev critical exponent. ...
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ژورنال
عنوان ژورنال: Communications on Pure and Applied Analysis
سال: 2010
ISSN: 1534-0392
DOI: 10.3934/cpaa.2011.10.527