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math.AP2020
Lipschitz Regularity in Vectorial Linear Transmission Problems
Alessio Figalli, Sunghan Kim, Henrik Shahgholian
We consider vector-valued solutions to a linear transmission problem, and we prove that Lipschitz-regularity on one phase is transmitted to the next phase. More exactly, given a so…
math.AP2020
Uniform Estimates in Periodic Homogenization of Fully Nonlinear Elliptic Equations
Sunghan Kim, Ki-Ahm Lee
This article is concerned with uniform and estimates in periodic homogenization of fully nonlinear elliptic equations. The analysis is based on the compactness…
math.AP2020
Nodal Sets for Broken Quasilinear Partial Differential Equations with Dini Coefficients
Sunghan Kim
This paper is concerned with the nodal set of weak solutions to a broken quasilinear partial differential equation, \begin{equation*} \mbox{div} (a_+ \nabla u^+ - a_- \nabla u^-) =…