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math.AP2024
Nonlocal elliptic equations involving logarithmic Laplacian: Existence, non-existence and uniqueness results
Rakesh Arora, Jacques Giacomoni, Arshi Vaishnavi
In this work, we study the existence, non-existence, and uniqueness results for nonlocal elliptic equations involving logarithmic Laplacian, and subcritical, critical, and supercri…
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…