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March/April 2015 Hölder estimates for second-order operators on domains with rough boundary
J. Rehberg, A.F.M. ter Elst
Adv. Differential Equations 20(3/4): 299-360 (March/April 2015).

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.

Citation

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J. Rehberg. A.F.M. ter Elst. "Hölder estimates for second-order operators on domains with rough boundary." Adv. Differential Equations 20 (3/4) 299 - 360, March/April 2015.

Information

Published: March/April 2015
First available in Project Euclid: 4 February 2015

zbMATH: 1316.35110
MathSciNet: MR3311436

Subjects:
Primary: 35A23, 35B65, 35D30, 35J25

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.20 • No. 3/4 • March/April 2015
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