2 citations · 2 across the 6 of their papers we have counts for
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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 $…
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…
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…
The Kato square root problem for parabolic operators with an anti-symmetric part in BMO
Alireza Ataei, Kaj Nyström
We solve the Kato square root problem for parabolic operators whose coefficients can be written as the sum of a complex part, which is coercive, and a real anti-symmetric part, whi…
The Kato square root problem for weighted parabolic operators
Alireza Ataei, Moritz Egert, Kaj Nyström
We give a simplified and direct proof of the Kato square root estimate for parabolic operators with elliptic part in divergence form and coefficients possibly depending on space an…