Global regularity for a class of fully nonlinear PDEs with unbalanced variable degeneracy

2023/05/14 by Elzon C. Bezerra Júnior, João Vitor da Silva, João Vítor da Silva +2 · 1 citation
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · doi:10.1112/jlms.12766

Abstract

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.

Citations

• C 1 , α regularity of solutions of some degenerate fully non-linear elliptic equations
• Regularity properties for p−dead core problems and their asymptotic limit as p→∞

Cited by

• Improved regularity estimates for degenerate or singular fully nonlinear dead-core systems and Hénon-type equations

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