Dirac--Sobolev Spaces and Sobolev Spaces

Details Dirac--Sobolev Spaces and Sobolev Spaces Dirac--Sobolev Spaces and Sobolev Spaces

2010-01-02

arxiv.org/abs/1001.0275v1

Mathematics

Analysis of PDEs

to appear in Funkcialaj Ekvacioj, 2010

Scientific paper

The aim of this work is to study the first order Dirac-Sobolev spaces in
$L^p$ norm on an open subset of ${\mathbb R}^3$ to clarify its relationship
with the corresponding Sobolev spaces. It is shown that for $1< p <\infty$,
they coincide, while for $p=1$, the latter spaces are proper subspaces of the
former.

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