Compactness properties and ground states for the affine Laplacian

2017/08/08 by Schindler, Ian, Tintarev, Cyril · 1 citation
#35H99 #35J20 #35J99 #46E30 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1708.02413

Abstract

The paper studies compactness properties of the affine Sobolev inequality of Gaoyong Zhang et al in the case p=2, and existence and regularity of related minimizers, in particular, solutions to the nonlocal Dirichlet problems -∑_i,j=1^N(A^-1[u])_ij(∂²u)/(∂ x_i∂ x_j)=f in Ω⊂\mathbb R^N, and -∑_i,j=1^N(A^-1[u])_ij(∂²u)/(∂ x_i∂ x_j)=u^q-1 , ugt;0, in Ω⊂\mathbb R^N, where A_ij[u]=∫_Ω(∂ u)/(∂ x_i)(∂ u)/(∂ x_j)dx and q∈(2,(2N)/(N-2)).

Cited by

• Higher-order affine Sobolev inequalities

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