## Calderón-Zygmund theory for parabolic obstacle problems with nonstandard growth

created by erhardt on 27 Jan 2014
modified on 05 Mar 2014

[BibTeX]

Published Paper

Inserted: 27 jan 2014
Last Updated: 5 mar 2014

We establish local Calderón-Zygmund estimates for solutions to certain parabolic problems with irregular obstacles and nonstandard $p(x,t)$-growth. More precisely, we will show that the spatial gradient $Du$ of the solution to the obstacle problem is as integrable as the obstacle $\psi$, i.e. $D\psi ^{p(\cdot)}, \partial_t\psi ^{\gamma_1'}\in L^q_\text{loc}~~~\Rightarrow~~~ Du ^{p(\cdot)}\in L^q_\text{loc},~~~\text{for any}~q>1,$ where $\gamma_1'=\frac{\gamma_1}{\gamma_1-1}$ and $\gamma_1$ is the lower bound for $p(\cdot)$.