Differentiability of Solutions to the Neumann Problem with Low-regularity Data via Dynamical Systems

Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 261)

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

Differentiability Lipschitz continuity weak solution elliptic equation divergence form co-normal boundary condition modulus of continuity square-Dini condition dynamical system asymptotically constant uniformly stable 

Mathematics Subject Classification (2010)

Primary 35A08 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsLinköping UniversityLinköpingSweden
  2. 2.RUDN UniversityMoscowRussia
  3. 3.Department of MathematicsNortheastern UniversityBostonUSA

Personalised recommendations