Advances in Differential Equations

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

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

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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

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

First available in Project Euclid: 4 February 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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