期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
卷 40, 期 3, 页码 1813-1846出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2020095
关键词
Parabolic Signorini problem; epiperimetric inequality; free boundary regularity; singular set
资金
- 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
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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