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

Daniel Wachsmuth

Let $u\in L^2(I;H^1(\Omega ))$ with ${\partial }_{t}u\in L^2(I;H^1(\Omega {)}^{\ast })$ be given. Then we show by means of a counter-example that the positive part $u^{+}$ of $u$ has less regularity, in p…