Some critical quasilinear elliptic problems with mixed Dirichlet–Neumann boundary conditions: Relation with Sobolev and Hardy–Sobolev optimal constants
Journal of Mathematical Analysis and Applications(2007)
摘要
In this paper we deal with the following mixed Dirichlet–Neumann elliptic problems(1){−div(|x|−pγ|∇u|p−2∇u)=λup−1|x|p(γ+1)+ur|x|(r+1)γ,u>0inΩ,u=0onΣ1,|x|−pγ|∇u|p−2∂u∂ν=0onΣ2 where Ω⊂RN (N⩾3) is a bounded domain such that 0∈Ω and with different choices of the parameters 1
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关键词
p-Laplacian like equations,Critical problems,Mixed boundary conditions,Optimal constants for Hardy–Sobolev inequalities
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