C1,α regularity of solutions of some degenerate fully non-linear elliptic equations

2012/01/18 by C. Imbert, Cyril Imbert, L. Silvestre +1 · 111 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Algorithm #Degenerate energy levels #Lipschitz continuity #Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Philosophy #Physics #Pure mathematics #Scroll #Theology #math.AP

paper · pdf · doi:10.1016/j.aim.2012.07.033

published in Advances in Mathematics 233(1), 196-206 (Elsevier BV) · Submitted

arxiv created 2012/01/18 · openalex publication_date 2012/11/03 · arxiv updated 2012/11/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In the present paper, a class of fully non-linear elliptic equations are considered, which are degenerate as the gradient becomes small. Hölder estimates obtained by the first author (2011) are combined with new Lipschitz estimates obtained through the Ishii-Lions method in order to get C^1,α estimates for solutions of these equations.

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• An overview of unconstrained free boundary problems. [europepmc]

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