Higher integrability for parabolic equations of $p(x,t)$-Laplacian type
S. N. Antont︠s︡ev, Vasilii Vasil'evich Zhikov · Advances in Differential Equations · 2005
Let $\Omega\subset\mathbb{R}^{n}$, $n\geq2$, be a bounded domain withboundary $\partial\Omega$, and $Q=\Omega\times(0,T]$ be a cylinder of height $Ts 0$ such that for every subdomain $Q^{\prime}$, $\overline{Q^{\prime}}\subset Q$, \[ \int_{Q^{\prime}}\left| abla u\right| ^{p(z)(1+ \varepsilon )}dz s <\infty. \]