Quantitative bounds for H\"older exponents in the Krylov--Safonov and Evans--Krylov theories
Jongmyeong Kim, Se-Chan Lee
TL;DR
This paper provides quantitative bounds on H"older exponents in key elliptic PDE theories when the ellipticity ratio approaches one, using Ishii--Lions and Schauder-type methods.
Contribution
It introduces new quantitative bounds for H"older exponents in Krylov--Safonov and Evans--Krylov theories near the ellipticity ratio of one.
Findings
Quantitative bounds established for H"older exponents
Analysis applies when ellipticity ratio is close to one
Utilizes Ishii--Lions and Schauder-type perturbation methods
Abstract
We establish quantitative bounds for H\"older exponents in the Krylov--Safonov and Evans--Krylov theories when the ellipticity ratio is close to one. Our analysis relies on the Ishii--Lions method for the Krylov--Safonov theory and a Schauder-type perturbation argument for the Evans--Krylov theory.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Mathematical Modeling in Engineering · Advanced Differential Equations and Dynamical Systems