Pointwise Boundary Differentiability for Fully Nonlinear Elliptic Equations
Duan Wu, Yuanyuan Lian, Kai Zhang
TL;DR
This paper establishes pointwise boundary differentiability for viscosity solutions of fully nonlinear elliptic equations, extending previous results for linear cases with more general geometric conditions and simplified proofs.
Contribution
It introduces a new, more general set of geometric conditions for boundary differentiability and provides simplified proofs for fully nonlinear elliptic equations.
Findings
Proves boundary differentiability for viscosity solutions
Generalizes previous linear results to nonlinear cases
Uses simplified proof techniques
Abstract
In this paper, we prove the pointwise boundary differentiability for viscosity solutions of fully nonlinear elliptic equations. This generalizes the previous related results for linear equations. The geometrical conditions in this paper are pointwise and more general than before. Moreover, our proofs are relatively simple.
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