Optimal regularity at the free boundary for the infinity obstacle problem

被引：20

作者：

Rossi, J. D. ^{[1
]}

Teixeira, E. V. ^{[2
]}

Urbano, J. M. ^{[3
]}

机构：

[1] Univ Alicante, Dept Math Anal, E-03080 Alicante, Spain

[2] Univ Fed Ceara, BR-60455760 Fortaleza, CE, Brazil

[3] Univ Coimbra, Dept Math, CMUC, P-3001501 Coimbra, Portugal

来源：

INTERFACES AND FREE BOUNDARIES | 2015年 / 17卷 / 03期

关键词：

Obstacle problem; infinity Laplacian; free boundary; optimal regularity; TUG-OF-WAR; LAPLACIAN;

D O I：

10.4171/IFB/347

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the obstacle problem for the infinity Laplacian. The main results are a characterization of the solution through comparison with cones that lie above the obstacle and the sharp C-1,C-1/3-regularity of the solutions at the free boundary.

引用

页码：381 / 398

页数：18

共 50 条

[1] Sharp results for the regularity and stability of the free boundary in the obstacle problem
Blank, I
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2001, 50 (03) : 1077 - 1112
[2] On the regularity of the free boundary in the p-Laplacian obstacle problem
Figalli, Alessio
Krummel, Brian
Ros-Oton, Xavier
JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (03) : 1931 - 1945
[3] Free Boundary Regularity in the Parabolic Fractional Obstacle Problem
Barrios, Begona
Figalli, Alessio
Ros-Oton, Xavier
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2018, 71 (10) : 2129 - 2159
[4] OPTIMAL REGULARITY AND FREE BOUNDARY REGULARITY FOR THE SIGNORINI PROBLEM
Andersson, J.
ST PETERSBURG MATHEMATICAL JOURNAL, 2013, 24 (03) : 371 - 386
[5] Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
Luis A. Caffarelli
Sandro Salsa
Luis Silvestre
Inventiones mathematicae, 2008, 171 : 425 - 461
[6] Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem
Danielli, Donatella
Garofalo, Nicola
Petrosyan, Arshak
To, Tung
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 249 (1181) : 1 - +
[7] Optimal Regularity in Rooftop-Like Obstacle Problem
Petrosyan, Arshak
To, Tung
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2010, 35 (07) : 1292 - 1325
[8] Regularity of the free boundary for the obstacle problem for the fractional Laplacian with drift
Garofalo, Nicola
Petrosyan, Arshak
Pop, Camelia A.
Garcia, Mariana Smit Vega
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2017, 34 (03): : 533 - 570
[9] Regularity of the free boundary in a neighborhood of a contact point in the obstacle problem
E. V. Zhelezina
Journal of Mathematical Sciences, 2000, 101 (2) : 2938 - 2940
[10] Optimal Regularity and Nondegeneracy of a Free Boundary Problem Related to the Fractional Laplacian
Ray Yang
Archive for Rational Mechanics and Analysis, 2013, 208 : 693 - 723

← 1 2 3 4 5 →