160 citations · 192 across the 13 of their papers we have counts for
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Porous Medium Flow with both a Fractional Potential Pressure and Fractional Time Derivative
Mark Allen, Luis Caffarelli, Alexis Vasseur
We study a porous medium equation with right hand side. The operator has nonlocal diffusion effects given by an inverse fractional Laplacian operator. The derivative in time is als…
A Fractional Free Boundary Problem Related to a Plasma Problem
Mark Allen
We study a fractional analogue of a plasma problem arising from physics. Specifically, for a fixed bounded domain we study solutions to the eigenfunction equation \[ (- Δ)^s u…
A Nondivergence Parabolic Problem with a Fractional Time derivative
Mark Allen
We study a nonlocal nonlinear parabolic problem with a fractional time derivative. We prove a Krylov-Safonov type result; mainly, we prove Holder regularity of solutions. Our esti…
A Parabolic Problem with a Fractional-Time Derivative
Mark Allen, Luis Caffarelli, Alexis Vasseur
We study regularity for a parabolic problem with fractional diffusion in space and a fractional time derivative. Our main result is a De Giorgi-Nash-Moser Holder regularity theorem…