Existence and global second-order regularity for anisotropic parabolic equations with variable growth

Rakesh Arora, Sergey Shmarev

We consider the homogeneous Dirichlet problem for the anisotropic parabolic equation \[ u_t-\sum_{i=1}^ND_{x_i}\left(|D_{x_i}u|^{p_i(x,t)-2}D_{x_i}u\right)=f(x,t) \] in the cylinde…