For a class of strongly elliptic, second order systems $L$ with rough coefficients on a Lipschitz domain $\Omega$, we show that if $Lu=0$ on $\Omega$ and $u$ vanishes on an open subset of the boundary, then weak a priori hypotheses on the nontangential maximal function of $u$
lead to strong estimates on $\nabla u$, in nontangential and Besov norms, near this subset.
Publié le : 2009-06-15
Classification:
Second order elliptic PDE,
Sobolev Besov spaces,
boundary regularity,
Lipschitz domains,
35J55,
35B65,
46E35,
31B25
@article{1246454027,
author = {Mitrea, Marius and Taylor, Michael},
title = {Local Regularity Results for Second Order Elliptic Systems on Lipschitz Domains},
journal = {Funct. Approx. Comment. Math.},
volume = {40},
number = {1},
year = {2009},
pages = { 175-184},
language = {en},
url = {http://dml.mathdoc.fr/item/1246454027}
}
Mitrea, Marius; Taylor, Michael. Local Regularity Results for Second Order Elliptic Systems on Lipschitz Domains. Funct. Approx. Comment. Math., Tome 40 (2009) no. 1, pp. 175-184. http://gdmltest.u-ga.fr/item/1246454027/