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Properties of the free boundaries for the obstacle problem of the porous medium equations.
- Source :
-
Advances in Calculus of Variations . Jan2024, Vol. 17 Issue 1, p209-235. 27p. - Publication Year :
- 2024
-
Abstract
- In this paper, we study the existence and interior W 2 , p -regularity of the solution, and the regularity of the free boundary ∂ { u > ϕ } to the obstacle problem of the porous medium equation, u t = Δ u m ( m > 1 ) with the obstacle function ϕ. The penalization method is applied to have the existence and interior regularity. To deal with the interaction between two free boundaries ∂ { u > ϕ } and ∂ { u > 0 } , we consider two cases on the initial data which make the free boundary ∂ { u > ϕ } separate from the free boundary ∂ { u > 0 } . Then the problem is converted into the obstacle problem for a fully nonlinear operator. Hence, the C 1 -regularity of the free boundary ∂ { u > ϕ } is obtained by the regularity theory of a class of obstacle problems for the general fully nonlinear operator. [ABSTRACT FROM AUTHOR]
- Subjects :
- *POROUS materials
*NONLINEAR operators
*EQUATIONS
*NONLINEAR equations
Subjects
Details
- Language :
- English
- ISSN :
- 18648258
- Volume :
- 17
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Advances in Calculus of Variations
- Publication Type :
- Academic Journal
- Accession number :
- 174631540
- Full Text :
- https://doi.org/10.1515/acv-2021-0113