Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 30, Tome 259 (1999), pp. 46-66
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M. Fuchs; M. Bildhauer. Regularity for dual solutions and for weak cluster points of minimizing sequences of variational problems with linear growth. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 30, Tome 259 (1999), pp. 46-66. http://geodesic.mathdoc.fr/item/ZNSL_1999_259_a2/
@article{ZNSL_1999_259_a2,
author = {M. Fuchs and M. Bildhauer},
title = {Regularity for dual solutions and for weak cluster points of minimizing sequences of variational problems with linear growth},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {46--66},
year = {1999},
volume = {259},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_259_a2/}
}
TY - JOUR
AU - M. Fuchs
AU - M. Bildhauer
TI - Regularity for dual solutions and for weak cluster points of minimizing sequences of variational problems with linear growth
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1999
SP - 46
EP - 66
VL - 259
UR - http://geodesic.mathdoc.fr/item/ZNSL_1999_259_a2/
LA - en
ID - ZNSL_1999_259_a2
ER -
%0 Journal Article
%A M. Fuchs
%A M. Bildhauer
%T Regularity for dual solutions and for weak cluster points of minimizing sequences of variational problems with linear growth
%J Zapiski Nauchnykh Seminarov POMI
%D 1999
%P 46-66
%V 259
%U http://geodesic.mathdoc.fr/item/ZNSL_1999_259_a2/
%G en
%F ZNSL_1999_259_a2
The minimum problem $\int_{\Omega}f(\nabla u)dx\longrightarrow\min$ among mappings $u:\mathbb R^n\supset\Omega\to\mathbb R^N$ with prescribed Dirichlet boundary data and for integrands $f$ of linear growth in general fails to have solutions in the Sobolev space $W^1_1$. We therefore concentrate on the dual variational problem which admits a unique maximizer $\sigma$ and prove partial Hölder continuity of $\sigma$. Moreover, we study smoothness properties of $L^1$-limits of minimizing sequences of the original problem.
