Regularity of a free boundary in parabolic potential theory

By Luis Caffarelli, Arshak Petrosyan, H. Shahgholian. 2004

104 citations recorded by the source corpus.

We study the regularity of the free boundary in a Stefan-type problem 1u − ∂t u = χ in D ⊂ Rn × R, u = |∇u| = 0 on D \ with no sign assumptions on u and the time derivative ∂t u.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6ab4e534106b65a479c9ced7fd1f535684fab4f6

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

On the continuity of the time derivative of the solution to the parabolic obstacle problem with variable coefficients (2006, background): “It has been for instance proved for the parabolic problem with constant coefficient in [7].”
Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem (2013, background): “] in the study of the elliptic thin obstacle problem. The rst family of monotonicity formulas goes back to the work of Weiss [Wei99a] in the elliptic case and [Wei99b] in the parabolic case; see also [CPS04]. Theorem 13.1 (Weiss-type monotonicity formula). Let u2Sf(S+ 1 ) with jf(x;t)j Mk(x;t)k‘ 2 i”
Regularity and Asymptotic Behavior of Nonlinear Stefan Problems (2014, unknown): “2 in [6] and then argue as in the proof of Lemma 4.”
A General Class of Free Boundary Problems for Fully Nonlinear Elliptic Equations (2012, result): “We also refer to several other articles concerning similar type of problems: For elliptic case see [5], [1], and for parabolic case see [6], [2].”