On a Minimization Problem Involving the Critical Sobolev Exponent
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AbstractFollowing [3] we study the following minimization problem:in any dimension n ≥ 4 and under suitable assumptions on a(x). Mainly we assume that a(x) belongs to the Lorentz space LN ≡ {x ∈ Ω|a(x) < 0}has positive Lebesgue measure. Notice that this last condition is satisfied when the set N has a nontrivial interior part (in fact this is the typical assumption imposed in the literature on the set N).
A minimization problem involving a critical sobolev exponent and its related Euler-Lagrange equation
1991 ◽
Vol 114
(4)
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pp. 365-381
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2004 ◽
Vol 290
(2)
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pp. 605-619
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2019 ◽
Vol 266
(11)
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pp. 7264-7290
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2017 ◽
Vol 40
(18)
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pp. 7255-7266
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