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math.AP2023
Existence and uniqueness of the solutions to convection-diffusion equations
Alireza Ataei
In this work, we study convection-diffusion equations in the cases of bounded drifts and drifts induced by the gradient of a potential. We define a new notion of solution and prove…
math.AP2023
A comparison method for the fractional Laplacian and applications
Alireza Ataei, Alireza Tavakoli
We study the boundary behavior of solutions to fractional elliptic equations. As the first result, the isolation of the first eigenvalue of the fractional Lane-Emden equation is pr…