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Lipschitz regularity of almost minimizers in a Bernoulli problem with non-standard growth
João Vitor da Silva, Analía Silva, Hernán Vivas
In this work we establish the optimal Lipschitz regularity for non-negative almost minimizers of the one-phase Bernoulli-type functional $$ \mathcal{J}_{\mathrm{G}}(u,Ω) := \int_Ω\…
Homogeneous eigenvalue problems in Orlicz-Sobolev spaces
Julian Fernandez Bonder, Ariel Salort, Hernan Vivas
In this article we consider a homogeneous eigenvalue problem ruled by the fractional Laplacian operator whose Euler-Lagrange equation is obtained by minimization of a quotient…
Free boundary regularity for a class of one-phase problems with non-homogeneous degeneracy
João Vítor da Silva, Giane C. Rampasso, Gleydson C. Ricarte +1
We consider a one-phase free boundary problem governed by doubly degenerate fully non-linear elliptic PDEs with non-zero right hand side, which should be understood as an analog (n…
Maximum principles, Liouville theorem and symmetry results for the fractional Laplacian
Sandra Molina, Ariel Salort, Hernán Vivas
We study different maximum principles for non-local non-linear operators with non-standard growth that arise naturally in the context of fractional Orlicz-Sobolev spaces and whose…
Sharp regularity for degenerate obstacle type problems: a geometric approach
João Vitor Da Silva, Hernán Vivas
We prove sharp regularity estimates for solutions of obstacle type problems driven by a class of degenerate fully nonlinear operators; more specifically, we consider viscosity solu…
regularity for fully nonlinear nonlocal equations with bounded right hand side
Hernán Vivas
We establish sharp interior regularity estimates for solutions of fully nonlinear nonlocal equations with bounded right hand side. More precisely, we show that if is a…