Monotonicity formulas for obstacle problems with Lipschitz coefficients

被引：15

作者：

Focardi, M. ^{[1
]}

Gelli, M. S. ^{[2
]}

Spadaro, E. ^{[3
]}

机构：

[1] Univ Florence, DiMaI U Dini, I-50134 Florence, Italy

[2] Univ Pisa, Dipartimento Matemat, I-56127 Pisa, Italy

[3] Max Planck Inst Math Nat Wissensch, D-04103 Leipzig, Germany

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2015年 / 54卷 / 02期

关键词：

NONLINEAR ELLIPTIC-EQUATIONS; FREE-BOUNDARY; 2-PHASE PROBLEMS; REGULARITY; 2ND-ORDER; OPERATORS; BEHAVIOR;

D O I：

10.1007/s00526-015-0835-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove quasi-monotonicity formulas for classical obstacle-type problems with energies being the sum of a quadratic form with Lipschitz coefficients, and a Holder continuous linear term. With the help of those formulas we are able to carry out the full analysis of the regularity of free-boundary points following the approaches by Caffarelli (J Fourier Anal Appl 4(4-5), 383-402, 1998), Monneau (J Geom Anal 13(2), 359-389, 2003), and Weiss (Invent Math 138(1), 23-50, 1999).

引用

页码：1547 / 1573

页数：27

共 31 条

[1] VARIATIONAL-PROBLEMS WITH 2 PHASES AND THEIR FREE BOUNDARIES [J].