Existence and non-existence of minimizers for Hardy-Sobolev type inequality with Hardy potentials

被引:0
作者
Chern, Jann-Long [1 ]
Hashizume, Masato [2 ]
Hwang, Gyeongha [3 ]
机构
[1] Natl Taiwan Normal Univ, Dept Math, Taipei, Taiwan
[2] Hiroshima Univ, Grad Sch Adv Sci & Engn, Higashihiroshima, Japan
[3] Yeungnam Univ, Dept Math, Gyongsan, South Korea
关键词
Semilinear elliptic equation; existence; non-existence; minimizers of Hardy-Sobolev type inequality; Hardy potential; CRITICAL ELLIPTIC-EQUATIONS; CRITICAL EXPONENTS; INTERPOLATION INEQUALITIES; SHARP CONSTANTS; SYMMETRY; PDES;
D O I
10.1080/00036811.2023.2268659
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Motivated by the Hardy-Sobolev inequality with multiple Hardy potentials,we consider the following minimization problem : inf{integral(Omega) |del u|(2) dx-lambda 1 integral(Omega) u(2)|x-P1|(2) dx -lambda(2)integral(Omega) u(2)|x-P-2|(2) dx| u is an element of H-0(1)(Omega),integral(Omega) |u|(2)|x|(s) dx = 1} whereN >= 3,is a smooth domain,lambda(1),lambda(2) is an element of R,0,P-1,P-2 is an element of Omega,s is an element of(0, 2) and 2(s)(*) = 2(N-s)N-2. Concerning the coefficients of Hardy potentials, we derive asharp threshold for the existence and non-existence of a minimizer. In addi-tion, we study the existence and non-existence of a positive solution to theEuler-Lagrangian equations corresponding to the minimization problems
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页码:1831 / 1845
页数:15
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