arXiv subjects

Thomas Backing

Publications and source records attributed to Thomas Backing.

2 recordsLinked to original sources

arXiv2015

Regularity of Solutions to a Parabolic Free Boundary Problem with Variable Coefficients

The main result of this paper is to prove that viscosity solutions to a parabolic free boundary problem with variable coefficients are Lipschitz continuous under the assumptions that the solution has a Lipschitz free boundary and satisfies a non-degeneracy condition. This is the optimal regularity for this problem.

math.AP↗

arXiv2015

Regularity of the Free Boundary for a Bernoulli-Type Parabolic Problem with Variable Coefficients

This paper studies the regularity of the free boundary for viscosity solutions to a parabolic Bernoulli-type free boundary problem with variable coefficients. The main result is that Lipschitz free boundaries are $C^1$ with a normal vector that varies with a Hölder modulus of continuity in both space and in time. As a consequence, the viscosity solution satisfies the free boundary problem in a classical sense.

math.AP↗