Advances in Differential Equations

Hölder estimates for second-order operators on domains with rough boundary

J. Rehberg and A.F.M. ter Elst

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper, we investigate linear elliptic, second-order boundary value problems with mixed boundary conditions on domains with a rough boundary. Assuming only boundedness/ellipticity on the coefficient function and very mild conditions on the geometry of the domain -- including a very weak compatibility condition between the Dirichlet boundary part and its complement -- we prove first Hölder continuity of the solution. Secondly, Gaussian Hölder estimates for the corresponding heat kernel are derived.

Article information

Source
Adv. Differential Equations Volume 20, Number 3/4 (2015), 299-360.

Dates
First available in Project Euclid: 4 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.ade/1423055203

Mathematical Reviews number (MathSciNet)
MR3311436

Subjects
Primary: 35J25: Boundary value problems for second-order elliptic equations 35B65: Smoothness and regularity of solutions 35D30: Weak solutions 35A23: Inequalities involving derivatives and differential and integral operators, inequalities for integrals

Citation

ter Elst, A.F.M.; Rehberg, J. Hölder estimates for second-order operators on domains with rough boundary. Adv. Differential Equations 20 (2015), no. 3/4, 299--360. https://projecteuclid.org/euclid.ade/1423055203.


Export citation