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math.AP2025
Modulus of continuity for solutions of non-local heat equations
Ben Andrews, Sophie Chen
We extend the two-point modulus-of-continuity method for parabolic equations---as used, for instance, in the proof of the fundamental gap conjecture---to non-local heat equations o…
math.AP2025
Counterexample to the second eigenfunction having one zero for a non-local Schrodinger operator
Ben Andrews, Sophie Chen
We demonstrate that the second eigenfunction of a perturbed fractional Laplace operator on a bounded interval can exhibit two sign changes, in stark contrast with the classical exp…
math.AP2005★ 13 cited
Local Estimates for Some Fully Nonlinear Elliptic Equations
Sophie Chen
We present a method to derive local estimates for some classes of fully nonlinear elliptic equations. The advantage of our method is that we derive Hessian estimates directly from…