Optimal limiting embeddings for $Δ$-reduced Sobolev spaces in $L^1$

Details Optimal limiting embeddings for $Δ$-reduced Sobolev spaces in $L^1$ Optimal limiting embeddings for $Δ$-reduced Sobolev spaces in $L^1$

2012-02-06

arxiv.org/abs/1202.1133v2

Mathematics

Functional Analysis

20 pages. In v2 the introduction is revised and extended in several places. References are added, in particular [AF] and [AC]

Scientific paper

We prove sharp embedding inequalities for certain reduced Sobolev spaces that
arise naturally in the context of Dirichlet problems with $L^1$ data. We also
find the optimal target spaces for such embeddings, which in dimension 2 could
be considered as limiting cases of the Hansson-Brezis-Wainger spaces, for the
optimal embeddings of borderline Sobolev spaces $W_0^{k,n/k}$.

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