arXiv subjects

Julio C. Correa

Publications and source records attributed to Julio C. Correa.

3 recordsLinked to original sources

arXiv2025

Two-phase free boundary problems for a class of fully nonlinear double-divergence systems

In this article, we study a class of fully nonlinear double-divergence systems with free boundaries associated with a minimization problem. The variational structure of Hessian-dependent functional plays a fundamental role in proving the existence of the minimizers and then the existence of the solutions for the system. In addition, we establish gains of the integrability for the double-divergence equation. Consequently, we improve the regularity for the fully nonlinear equation in Sobolev and Hölder spaces.

math.AP↗

arXiv2025

A two-phase quenching-type problem for the p-Laplacian

We study minimizers of non-differentiable functionals of the Alp-Phillips type with two-phases for the $p$-Laplacian , focusing on the geometric and analytical properties of free boundaries. The main result establishes finite $(n-1)$-dimensional Hausdorff measure estimates, achieved through optimal gradient decay estimates, a $BV$-inequality and the known classifications of blow-up profiles of the linear case.

math.AP↗

arXiv2023

A Hessian-dependent functional with free boundaries and applications to mean-field games

We study a Hessian-dependent functional driven by a fully nonlinear operator. The associated Euler-Lagrange equation is a fully nonlinear mean-field game with free boundaries. Our findings include the existence of solutions to the mean-field game, together with Hölder continuity of the value function and improved integrability of the density. In addition, we prove the reduced free boundary is a set of finite perimeter. To conclude our analysis, we prove a $Γ$-convergence result for the functional.

math.AP↗