8 papers · 1 filter
Fractional -curvature on the sphere and optimal partitions
Héctor A. Chang-Lara, Juan Carlos Fernández, Alberto Saldaña
We study an optimal partition problem on the sphere, where the cost functional is associated with the fractional -curvature in terms of the conformal fractional Laplacian on the…
A Visual Approach to the Regularity Theory for Fully Nonlinear Elliptic Equations
Héctor A. Chang-Lara
We revisit the regularity theory for uniformly elliptic equations.
Well-posedness for a transmission problem connecting first and second-order operators
Héctor A. Chang-Lara
We establish the existence and uniqueness of viscosity solutions within a domain for a class of equations governed by elliptic and eikonal type equations in…
Non-convex Hamilton-Jacobi equations with gradient constraints
Héctor A. Chang-Lara, Edgard A. Pimentel
We study non-convex Hamilton-Jacobi equations in the presence of gradient constraints and produce new, optimal, regularity results for the solutions. A distinctive feature of those…
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…
Boundary Regularity for the Free Boundary in the One-phase Problem
Hector Chang-Lara, Ovidiu Savin
We consider the Bernoulli one-phase free boundary problem in a domain and show that the free boundary is regular in a neighborhood of the fixed boundary $\parti…