On higher order boundary Harnack and analyticity of free boundaries

Abstract

We establish a C^1,alpha Schauder estimate of a non-standard degenerate elliptic equation and use it to give another proof of the higher order boundary Harnack inequality. As an application, we obtain the analyticity of the free boundary in the classical obstacle problem based on iterating the boundary Harnack principle.

References in corpus (4)

• Higher order boundary Harnack principle via degenerate equations
• On parabolic and elliptic equations with singular or degenerate coefficients
• On the analyticity of solutions to non-linear elliptic partial differential equations
• Weighted mixed-norm $L_p$ estimates for equations in non-divergence form with singular coefficients: the Dirichlet problem

Cited by in corpus (1)

• Higher order boundary Harnack principles in Dini type domains