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Higher regularity of the free boundary in the parabolic Signorini problem | | Agnid Banerjee
; Mariana Smit Vega Garcia
; Andrew K. Zeller
; | | Date: |
12 Jan 2016 | | Abstract: | We show that the quotient of two caloric functions which vanish on a portion
of an $H^{k+ alpha}$ regular slit is $H^{k+ alpha}$ at the slit, for $k geq
2$. In the case $k=1$, we show that the quotient is in $H^{1+alpha}$ if the
slit is assumed to be space-time $C^{1, alpha}$ 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 $C^{infty}$ regular in space and time. | | Source: | arXiv, 1601.2976 | | Services: | Forum | Review | PDF | Favorites | |
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