1 citations · 3 across the 4 of their papers we have counts for
9 papers
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…
Weak Limits of Fractional Sobolev Homeomorphisms are Almost Injective: A Note
Armin Schikorra, James M. Scott
Let be an open set and be a sequence of homeomorphisms weakly converging to . It is known t…
The Solvability of a Strongly-Coupled Nonlocal System of Equations
Tadele Mengesha, James M. Scott
We prove existence and uniqueness of strong (pointwise) solutions to a linear nonlocal strongly coupled hyperbolic system of equations posed on all of Euclidean space. The system o…
Analysis of the Zero Relaxation Limit of Systems of Hyperbolic Conservation Laws with Random Initial Data
James M. Scott, M. Paul Laiu, Cory D. Hauck
We show the convergence of the zero relaxation limit in systems of hyperbolic conservation laws with stochastic initial data. Precisely, solutions converge to a soluti…