Second order Sobolev regularity for normalized parabolic $p(x)$-Laplace equations via the algebraic structure

Yuqing Wang, Yizhe Zhu

Denote by $\Delta$ the Laplacian and by ${\Delta }_{\infty }$ the $\infty$-Laplacian. A fundamental inequality is proved for the algebraic structure of $\Delta v{\Delta }_{\infty }v$: for every $v\in C^{\infty }$,…