Hölder estimates for parabolic operators on domains with rough boundary
- Disser, Karoline
- Rehberg, Joachim
- ter Elst, A. F. M.
2010 Mathematics Subject Classification
- 35K20 35B45 35B65 35B05
- Parabolic initial boundary value problems, Hölder continuity
In this paper we investigate linear parabolic, second-order boundary value problems with mixed boundary conditions on rough domains. 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 Hölder continuity of the solution in space and time.
- Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), XVII (2017), pp. 65--79.