Optimal global second-order regularity and improved integrability for parabolic equations with variable growth

Rakesh Arora, Sergey Shmarev

We consider the homogeneous Dirichlet problem for the parabolic equation \[ u_t- \operatorname{div} \left(|\nabla u|^{p(x,t)-2} \nabla u\right)= f(x,t) + F(x,t, u, \nabla u) \] in…