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The regularity theory for the parabolic double obstacle problem

Authors :
Jinwan Park
Ki-Ahm Lee
Source :
Mathematische Annalen. 381:685-728
Publication Year :
2020
Publisher :
Springer Science and Business Media LLC, 2020.

Abstract

In this paper, we study the regularity of the free boundaries of the parabolic double obstacle problem for the heat operator and fully nonlinear operator. The result in this paper are generalizations of the theory for the elliptic problem in Lee et al. (Calc Var Partial Differ Equ 58(3):104, 2019) and Lee and Park (The regularity theory for the double obstacle problem for fully nonlinear operator, , 2018) to parabolic case and also the theory for the parabolic single obstacle problem in Caffarelli et al. (J Am Math Soc 17(4):827–869, 2004) to double obstacle case. New difficulties in the theory which are generated by the characteristic of parabolic PDEs and the existence of the upper obstacle are discussed in detail. Furthermore, the thickness assumptions to have the regularity of the free boundary are carefully considered.

Details

ISSN :
14321807 and 00255831
Volume :
381
Database :
OpenAIRE
Journal :
Mathematische Annalen
Accession number :
edsair.doi...........b0e49636b4093defc09872092a8dbc2a