Advances in Differential Equations
- Adv. Differential Equations
- Volume 20, Number 3/4 (2015), 299-360.
Hölder estimates for second-order operators on domains with rough boundary
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.
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)
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. https://projecteuclid.org/euclid.ade/1423055203