Comparison principles and Lipschitz regularity for some nonlinear degenerate elliptic equations

被引：26

作者：

Li, YanYan ^{[1
,2
]}

Luc Nguyen ^{[3
,4
]}

Wang, Bo ^{[5
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[2] Rutgers State Univ, Dept Math, 110 Frelinghuysen Rd, Piscataway, NJ 08854 USA

[3] Univ Oxford, Math Inst, Andrew Wiles Bldg,Woodstock Rd, Oxford OX2 6GG, England

[4] Univ Oxford, St Edmund Hall, Andrew Wiles Bldg,Woodstock Rd, Oxford OX2 6GG, England

[5] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2018年 / 57卷 / 04期

关键词：

STRONG MAXIMUM PRINCIPLE; VISCOSITY SOLUTIONS; CONFORMALLY INVARIANT; HARNACK INEQUALITIES; SINGULAR SOLUTIONS; YAMABE PROBLEM; EXISTENCE; EIGENVALUES; SETS;

D O I：

10.1007/s00526-018-1369-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish interior Lipschitz regularity for continuous viscosity solutions of fully nonlinear, conformally invariant, degenerate elliptic equations. As a by-product of our method, we also prove a weak form of the strong comparison principle, which we refer to as the principle of propagation of touching points, for operators of the form which are non-decreasing in .

引用

页数：29

共 45 条

[1] Amendola ME, 2013, DIFFER INTEGRAL EQU, V26, P845
[2] [Anonymous], 1988, Rev. Mat. Iberoam.
[3] [Anonymous], 1992, Bull. Amer. Math. Soc.
[4] On the strong maximum principle for fully nonlinear degenerate elliptic equations
Bardi, M
Da Lio, F
[J]. ARCHIV DER MATHEMATIK, 1999, 73 (04) : 276 - 285
[5] Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators
Berestycki, Henri
Dolcetta, Italo Capuzzo
Porretta, Alessio
Rossi, Luca
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2015, 103 (05): : 1276 - 1293
[6] Eigenvalue, maximum principle and regularity for fully non linear homogeneous operators
Birindelli, I.
Demengel, F.
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2007, 6 (02) : 335 - 366
[7] Birindelli I., 2004, Ann. Fac. Sci. Toulouse Math., V13, P261, DOI 10.5802/afst.1070
[8] Cabre X., 1995, Topol. Methods Nonlinear Anal., V6, P31, DOI DOI 10.12775/TMNA.1995.030
[9] THE DIRICHLET PROBLEM FOR NONLINEAR 2ND-ORDER ELLIPTIC-EQUATIONS .3. FUNCTIONS OF THE EIGENVALUES OF THE HESSIAN
CAFFARELLI, L
NIRENBERG, L
SPRUCK, J
[J]. ACTA MATHEMATICA, 1985, 155 (3-4) : 261 - 301
[10] Some Remarks on Singular Solutions of Nonlinear Elliptic Equations III: Viscosity Solutions Including Parabolic Operators
Caffarelli, Luis
Li, Yanyan
Nirenberg, Louis
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2013, 66 (01) : 109 - 143

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