Sharp regularity for a singular fully nonlinear parabolic free boundary problem

Damião J. Araújo; Ginaldo S. Sá; José Miguel Urbano

doi:10.1016/j.jde.2024.01.013

Sharp regularity for a singular fully nonlinear parabolic free boundary problem

Damião J. Araújo, Ginaldo S. Sá, José Miguel Urbano^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

This paper establishes sharp local regularity estimates for viscosity solutions of fully nonlinear parabolic free boundary problems with singular absorption terms. The main difficulties are due to the blow-up of the source along the free boundary and the lack of a variational structure. The proof combines the power of the Ishii-Lions method with intrinsically parabolic oscillation estimates. The results are new, even for second-order linear operators in nondivergence form.

Original language	English (US)
Pages (from-to)	90-113
Number of pages	24
Journal	Journal of Differential Equations
Volume	389
DOIs	https://doi.org/10.1016/j.jde.2024.01.013
State	Published - Apr 25 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Inc.

Keywords

Free boundary
Sharp regularity
Singular parabolic PDEs
Viscosity solutions

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2024.01.013

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title = "Sharp regularity for a singular fully nonlinear parabolic free boundary problem",

abstract = "This paper establishes sharp local regularity estimates for viscosity solutions of fully nonlinear parabolic free boundary problems with singular absorption terms. The main difficulties are due to the blow-up of the source along the free boundary and the lack of a variational structure. The proof combines the power of the Ishii-Lions method with intrinsically parabolic oscillation estimates. The results are new, even for second-order linear operators in nondivergence form.",

keywords = "Free boundary, Sharp regularity, Singular parabolic PDEs, Viscosity solutions",

author = "Ara{\'u}jo, {Dami{\~a}o J.} and S{\'a}, {Ginaldo S.} and Urbano, {Jos{\'e} Miguel}",

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year = "2024",

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doi = "10.1016/j.jde.2024.01.013",

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T1 - Sharp regularity for a singular fully nonlinear parabolic free boundary problem

AU - Araújo, Damião J.

AU - Sá, Ginaldo S.

AU - Urbano, José Miguel

PY - 2024/4/25

Y1 - 2024/4/25

N2 - This paper establishes sharp local regularity estimates for viscosity solutions of fully nonlinear parabolic free boundary problems with singular absorption terms. The main difficulties are due to the blow-up of the source along the free boundary and the lack of a variational structure. The proof combines the power of the Ishii-Lions method with intrinsically parabolic oscillation estimates. The results are new, even for second-order linear operators in nondivergence form.

AB - This paper establishes sharp local regularity estimates for viscosity solutions of fully nonlinear parabolic free boundary problems with singular absorption terms. The main difficulties are due to the blow-up of the source along the free boundary and the lack of a variational structure. The proof combines the power of the Ishii-Lions method with intrinsically parabolic oscillation estimates. The results are new, even for second-order linear operators in nondivergence form.

KW - Free boundary

KW - Sharp regularity

KW - Singular parabolic PDEs

KW - Viscosity solutions

UR - http://www.scopus.com/inward/record.url?scp=85183123698&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2024.01.013

DO - 10.1016/j.jde.2024.01.013

M3 - Article

AN - SCOPUS:85183123698

SN - 0022-0396

VL - 389

SP - 90

EP - 113

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Sharp regularity for a singular fully nonlinear parabolic free boundary problem

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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