Differentiability of Solutions to the Neumann Problem with Low-Regularity Data via Dynamical Systems
Analysis of PDEs
2016-02-18 v1
Abstract
We obtain conditions for the differentiability of weak solutions for a second-order uniformly elliptic equation in divergence form with a homogeneous co-normal boundary condition. The modulus of continuity for the coefficients is assumed to satisfy the square-Dini condition and the boundary is assumed to be differentiable with derivatives also having this modulus of continuity. Additional conditions for the solution to be Lipschitz continuous or differentiable at a point on the boundary depend upon the stability of a dynamical system that is derived from the coefficients of the elliptic equation.
Keywords
Cite
@article{arxiv.1602.05210,
title = {Differentiability of Solutions to the Neumann Problem with Low-Regularity Data via Dynamical Systems},
author = {Robert McOwen and Vladimir Maz'ya},
journal= {arXiv preprint arXiv:1602.05210},
year = {2016}
}
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34 pages