Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volume 40, Issue 3, Pages 1813-1846Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2020095
Keywords
Parabolic Signorini problem; epiperimetric inequality; free boundary regularity; singular set
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Funding
- Portuguese Government through FCT/MCTES [CMUC - UID/MAT/00324/2013]
- European Regional Development Fund through the Partnership Agreement PT2020
- FCT [TUBITAK/0005/2014]
- DFG individual research grant [SH 1403/1-1]
- Fundação para a Ciência e a Tecnologia [TUBITAK/0005/2014] Funding Source: FCT
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In this note, we use an epiperimetric inequality approach to study the regularity of the free boundary for the parabolic Signorini problem. We show that if the vanishing order of a solution at a free boundary point is close to 3/2 or an even integer, then the solution is asymptotically homogeneous. Furthermore, one can derive a convergence rate estimate towards the asymptotic homogeneous solution. As a consequence, we obtain the regularity of the regular free boundary as well as the frequency gap.
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