2023/05/14 by Elzon C. Bezerra Júnior, João Vitor da Silva, João Vítor da Silva +2 · 10 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Applied mathematics #Bounded function #Class (philosophy) #Compact space #Computer science #Degeneracy (biology) #Degenerate energy levels #Function (biology) #Geometry #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Nonlinear system #Open set #Partial differential equation #Physics #Pure mathematics #Scaling #Stability and Controllability of Differential Equations #Variable (mathematics)
paper · doi:10.1112/jlms.12766
published in Journal of the London Mathematical Society 108(2), 622-665 (Wiley)
openalex publication_date 2023/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Abstract We establish the existence and sharp global regularity results (, and estimates) for a class of fully nonlinear elliptic Partial Differential Equations (PDEs) with unbalanced variable degeneracy. In a precise way, the degeneracy law of the model switches between two different kinds of degenerate elliptic operators of variable order, according to the null set of a modulating function . The model case in question is given by for a bounded, regular, and open set , and appropriate continuous data , , and . Such sharp regularity estimates generalize and improve, to some extent, earlier ones via geometric treatments. Our results are consequences of geometric tangential methods and make use of compactness, localized oscillating, and scaling techniques. In the end, our findings are applied in the study of a wide class of nonlinear models.