5 citations · 11 across the 8 of their papers we have counts for
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Hardy's inequality and (almost) the Landau equation
Maria Gualdani, Nestor Guillen
In this manuscript we establish an estimate for the isotropic analogue of the homogeneous Landau equation. This is done for values of the interaction exponent in (a…
Optimal transport and the Gauss curvature equation
Nestor Guillen, Jun Kitagawa
In this short note, we consider the problem of prescribing the Gauss curvature and image of the Gauss map for the graph of a function over a domain in Euclidean space. The prescrip…
Min-max formulas for nonlocal elliptic operators on Euclidean space
Nestor Guillen, Russell Schwab
An operator satisfies the Global Comparison Property if anytime a function touches another from above at some point, then the operator preserves the ordering at the point of contac…
Some free boundary problems recast as nonlocal parabolic equations
Hector A. Chang-Lara, Nestor Guillen, Russell W. Schwab
In this work we demonstrate that a class of some one and two phase free boundary problems can be recast as nonlocal parabolic equations on a submanifold. The canonical examples wou…
Coupling Levy measures and comparison principles for viscosity solutions
Nestor Guillen, Chenchen Mou, Andrzej Swiech
We prove new comparison principles for viscosity solutions of non-linear integro-differential equations. The operators to which the method applies include but are not limited to th…
Estimates for Dirichlet-to-Neumann maps as integro-differential operators
Nestor Guillen, Jun Kitagawa, Russell W. Schwab
Some linear integro-differential operators have old and classical representations as the Dirichlet-to-Neumann operators for linear elliptic equations, such as the 1/2-Laplacian or…