The structure of the singular set in the thin obstacle problem for degenerate parabolic equations

被引：16

作者：

Banerjee, Agnid ^{[1
]}

Daniel, Donatelia ^{[2
]}

Garofalo, Nicola ^{[3
]}

Petrosyan, Arshak ^{[4
]}

机构：

[1] TIFR CAM, Bangalore 560065, Karnataka, India

[2] Arizona State Univ, Sch Math & Stat Sci, 900 S Palm, Walk Tempe, AZ 85281 USA

[3] Univ Padua, Dipartimento Ingn Civile Edile & Ambientale DICEA, I-35131 Padua, Italy

[4] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2021年 / 60卷 / 03期

关键词：

FREE-BOUNDARY; EXTENSION PROBLEM; REGULARITY; MONOTONICITY;

D O I：

10.1007/s00526-021-01938-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the singular set in the thin obstacle problem for degenerate parabolic equations with weight vertical bar y vertical bar(a) for a is an element of (-1, 1). Such problem arises as the local extension of the obstacle problem for the fractional heat operator (partial derivative(t) - Delta(x))(s) for s is an element of (0, 1). Our main result establishes the complete structure and regularity of the singular set of the free boundary. To achieve it, we prove Almgren-Poon, Weiss, and Monneau type monotonicity formulas which generalize those for the case of the heat equation (a = 0).

引用

页数：52

共 20 条

[1]

Athanasopoulos I, 2019, ANN SCUOLA NORM-SCI, V19, P781

[2] On the regularity of the non-dynamic parabolic fractional obstacle problem [J].