Higher regularity of the free boundary in the parabolic Signorini problem

2016/01/12 by Banerjee, Agnid, Garcia, Mariana Smit Vega, Zeller, Andrew K.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1601.02976

Abstract

We show that the quotient of two caloric functions which vanish on a portion of an H^{k+ α} regular slit is H^{k+ α} at the slit, for k ≥ 2. In the case k=1, we show that the quotient is in H^1+α if the slit is assumed to be space-time C^{1, α} regular. This can be thought of as a parabolic analogue of a recent important result in [DSS14a], whose ideas inspired us. As an application, we show that the free boundary near a regular point of the parabolic thin obstacle problem studied in [DGPT] with zero obstacle is C^∞ regular in space and time.

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• Free boundary regularity for almost minimizers of the parabolic Signorini problem
• The regular free boundary in the thin obstacle problem for degenerate parabolic equations
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• Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem
• Optimal Regularity for the parabolic No-Sign Obstacle Problem