2 citations · 6 across the 21 of their papers we have counts for
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A note on estimates of level sets and their role in demonstrating regularity of solutions to nonlocal double phase equations
James M. Scott, Tadele Mengesha
In this note we prove an estimate on the level sets of a function with growth that depends on the difference quotient of a bounded weak solution to a nonlocal double phase…
A Fractional Korn-type inequality for smooth domains and a regularity estimate for nonlinear nonlocal systems of equations
Tadele Mengesha, James M. Scott
In this paper we prove a fractional analogue of the classical Korn's first inequality. The inequality makes it possible to show the equivalence of a function space of vector field…
Self-improving Inequalities for bounded weak solutions to nonlocal double phase equations
James M. Scott, Tadele Mengesha
We prove higher Sobolev regularity for bounded weak solutions to a class of nonlinear nonlocal integro-differential equations. The leading operator exhibits nonuniform growth, swit…
The Darcy problem with porosity depending exponentially on the pressure
Zerihun Kinfe Birhanu, Tadele Mengesha, Abner J. Salgado
We consider the flow of a viscous incompressible fluid through a porous medium. We allow the permeability of the medium to depend exponentially on the pressure and provide an analy…
Calderon-Zygmund type estimates for nonlocal PDE with Hölder continuous kernel
Tadele Mengesha, Armin Schikorra, Sasikarn Yeepo
We study interior -regularity theory, also known as Calderon-Zygmund theory, of the equation \[ \int_{\mathbb{R}^n} \int_{\mathbb{R}^n} \frac{K(x,y)\ (u(x)-u(y))\, (φ(x)-φ(y))…