Regularity for a special case of two-phase Hele-Shaw flow via parabolic integro-differential equations
Abstract
We establish that the regularity theory for translation invariant fractional order parabolic integro-differential equations (via Krylov-Safonov estimates) gives an improvement of regularity mechanism for solutions to a special case of a two-phase free boundary flow related to Hele-Shaw. The special case is due to both a graph assumption on the free boundary of the flow and an assumption that the free boundary is in space. The free boundary then must immediately become for a universal depending upon the Dini modulus of the gradient of the graph. These results also apply to one-phase problems of the same type.
Keywords
Cite
@article{arxiv.2008.01272,
title = {Regularity for a special case of two-phase Hele-Shaw flow via parabolic integro-differential equations},
author = {Farhan Abedin and Russell W. Schwab},
journal= {arXiv preprint arXiv:2008.01272},
year = {2020}
}
Comments
Modified the presentation of Theorem 1.2 to make more clear the dependence of the constants on various parameters and norms. Fixed various typos