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On a Singular Variational Problem

Author: TanJingGang
Tutor: YangJianFu
School: Wuhan Institute of Physics and Institute of Mathematics
Course: Basic mathematics
Keywords: Hardy inequality elliptic equation concentration-compactness principle
CLC: O176
Type: Master's thesis
Year: 2003
Downloads: 16
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In this paper, we deal with the singular variational problems: S(a,b,λ0):=(?)∫RN(|x|-am|▽u|m0|x|-(a+1)m|u|m)dx/∫RN|x|-bp|u|pdx)m/p,as well as (?)=(?)(b,bλ1,λ2):=(?)∫RNJ(v,v)dx/(∫RN|x|-bp|u|α|u|βdx)m/p,where J(u, v)=|x|-am|▽u|m1|x|(-(a+1)m|u|m+|x|-am|▽v|m2|x|-(a+1)m|v|m,N≥m+1>2, 0≤a<N-m/m,a≤b<a+1 and p=p(a,b)=α+β=Nm/N-m+m(b-a),α,β≥1, E≡Da 1,m(RN). The aim of this paper is to show the exis-tence of minimizer for S(a, b,λ0) and (?)(a, b,λ12).

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Calculus of variations
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