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math.AP2024
Global gradient estimates for solutions of parabolic equations with nonstandard growth
Rakesh Arora, Sergey Shmarev
We study how the smoothness of the initial datum and the free term affect the global regularity properties of solutions to the Dirichlet problem for the class of parabolic equation…
math.AP2022
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…