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G. C. Ricarte

Publications and source records attributed to G. C. Ricarte.

5 recordsLinked to original sources
arXiv2024

High-Order regularity for fully nonlinear elliptic transmission problems under weak convexity assumption

This paper studies Schauder theory to transmission problems modelled by fully nonlinear uniformly elliptic equations of second order. We focus on operators F that fails to be concave or convex in the space of symmetric matrices. In a first scenario, it is considered that F enjoys a small ellipticity aperture. In our second case, we study regularity results where the convexity of the superlevel (or sublevel) sets is verified, implying that the operator F is quasiconcave (or quasiconvex).

math.AP↗
arXiv2020

Geometric Gradient Estimates For Fully Nonlinear Models With Non-Homogeneous Degeneracy and Applications

We establish sharp geometric Holder regularity estimates for Gradient for bounded solutions of a class of fully nonlinear elliptic equations with non-homogeneous degeneracy. Such regularity estimates simplify and generalize, to some extent, earlier ones via a totally different modus operandi. Our approach is based on geometric tangential methods and makes use of a refined oscillation mechanism combined with compactness and scaling techniques. In the end, we present some connections of our findings with a variety of nonlinear geometric free boundary problems and relevant nonlinear problems in the theory of elliptic PDEs, which may have their own interest. We also deliver explicit examples where our results are sharp.

math.AP↗
arXiv2020

Geometric regularity estimates for fully nonlinear elliptic equations with free boundaries

In this manuscript we study geometric regularity estimates for problems driven by fully nonlinear elliptic operators under strong absorption conditions. We establish improved geometric regularity along the free boundary, for a sharp value depending only on structural parameters. Non degeneracy among others measure theoretical properties are also obtained. A sharp Liouville result for entire solutions with controlled growth at infinity is proved. We also present a number of applications consequential of our findings.

math.AP↗