The regularity of the positive part of functions in $L^2(I;H^1\left(\Omega \right))\cap H^1(I;H^1{\left(\Omega \right)}^{*})$ with applications to parabolic equations

Wachsmuth, Daniel. "The regularity of the positive part of functions in $L^2(I; H^1(\Omega )) \cap H^1(I; H^1(\Omega )^*)$ with applications to parabolic equations." Commentationes Mathematicae Universitatis Carolinae 57.3 (2016): 327-332. <http://eudml.org/doc/286847>.

@article{Wachsmuth2016,
abstract = {Let $u\in L^2(I; H^1(\Omega ))$ with $\partial _t u\in L^2(I; H^1(\Omega )^*)$ be given. Then we show by means of a counter-example that the positive part $u^+$ of $u$ has less regularity, in particular it holds $\partial _t u^+ \notin L^1(I; H^1(\Omega )^*)$ in general. Nevertheless, $u^+$ satisfies an integration-by-parts formula, which can be used to prove non-negativity of weak solutions of parabolic equations.},
author = {Wachsmuth, Daniel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Bochner integrable function; projection onto non-negative functions; parabolic equation},
language = {eng},
number = {3},
pages = {327-332},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The regularity of the positive part of functions in $L^2(I; H^1(\Omega )) \cap H^1(I; H^1(\Omega )^*)$ with applications to parabolic equations},
url = {http://eudml.org/doc/286847},
volume = {57},
year = {2016},
}

TY - JOUR
AU - Wachsmuth, Daniel
TI - The regularity of the positive part of functions in $L^2(I; H^1(\Omega )) \cap H^1(I; H^1(\Omega )^*)$ with applications to parabolic equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 3
SP - 327
EP - 332
AB - Let $u\in L^2(I; H^1(\Omega ))$ with $\partial _t u\in L^2(I; H^1(\Omega )^*)$ be given. Then we show by means of a counter-example that the positive part $u^+$ of $u$ has less regularity, in particular it holds $\partial _t u^+ \notin L^1(I; H^1(\Omega )^*)$ in general. Nevertheless, $u^+$ satisfies an integration-by-parts formula, which can be used to prove non-negativity of weak solutions of parabolic equations.
LA - eng
KW - Bochner integrable function; projection onto non-negative functions; parabolic equation
UR - http://eudml.org/doc/286847
ER -