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math.AP2023★ 2 cited
Boundary behavior of solutions to fractional -Laplacian equation
Alireza Ataei
In this work, a generalized Hopf's lemma and a global boundary Harnack inequality are proved for solutions to fractional -Laplacian equations. Then, the isolation of the first $…
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…
math.AP2023
On fundamental solutions and Gaussian bounds for degenerate parabolic equations with time-dependent coefficients
Alireza Ataei, Kaj Nyström
We consider second order degenerate parabolic equations with real, measurable, and time-dependent coefficients. We allow for degenerate ellipticity dictated by a spatial -weig…