Regularity of fully non-linear elliptic equations on Kahler cones

被引：0

作者：

Yuan, Rirong ^{[1
]}

机构：

[1] South China Univ Technol, Sch Math, Guangzhou 510641, Peoples R China

来源：

PURE AND APPLIED MATHEMATICS QUARTERLY | 2020年 / 16卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Dirichlet problem; degenerate fully non-linear elliptic equations; quantitative boundary estimate; gradient estimate; cone condition; Sasakian manifolds; COMPLEX MONGE-AMPERE; BOUNDARY-VALUE-PROBLEMS; DIRICHLET PROBLEM; PARABOLIC EQUATIONS; GAUDUCHON METRICS; CURVATURE; SURFACES; SPACE;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive quantitative boundary estimates, and then solve the Dirichlet problem for a general class of fully non-linear elliptic equations on annuli of Kahler cones over closed Sasakian manifolds. This extends extensively a result concerning the geodesic equations in the space of Sasakian metrics due to Guan-Zhang. Our results show that the solvability is deeply affected by the transverse Kahler structures of Sasakian manifolds. We also discuss possible extensions of the results to equations with right-hand side depending on unknown solutions.

引用

页码：1609 / 1641

页数：33

共 50 条

[41] EXISTENCE AND REGULARITY PROBLEMS FOR NON-LINEAR FUNCTIONAL-EQUATIONS
SWIATAK, H
ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1977, 30 (1-2): : 21 - 31
[42] REGULARITY OF SOLUTIONS OF FULLY NONLINEAR ELLIPTIC-EQUATIONS
TRUDINGER, NS
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 1984, 3A (03): : 421 - 430
[43] On the regularity of viscosity solutions of fully nonlinear elliptic equations
Kovats, Jay
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 63 (5-7) : E1341 - E1350
[44] New regularity estimates for fully nonlinear elliptic equations
Nascimento, Thialita M.
Teixeira, Eduardo V.
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2023, 171 : 1 - 25
[45] Fractional Sobolev regularity for fully nonlinear elliptic equations
Pimentel, Edgard A.
Santos, Makson S.
Teixeira, Eduardo, V
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2022, 47 (08) : 1539 - 1558
[46] THE LOCALIZATION OF SOLUTIONS TO NON-LINEAR DEGENERATING ELLIPTIC AND PARABOLIC EQUATIONS
ANTONTSEV, SN
DOKLADY AKADEMII NAUK SSSR, 1981, 260 (06): : 1289 - 1293
[47] TOPOLOGICAL METHODS FOR NON-LINEAR ELLIPTIC EQUATIONS OF ARBITRARY ORDER
BROWDER, FE
PACIFIC JOURNAL OF MATHEMATICS, 1966, 17 (01) : 17 - &
[48] ON SOME NON-LINEAR ELLIPTIC DIFFERENTIAL-FUNCTIONAL EQUATIONS
HARTMAN, P
STAMPACCHIA, G
ACTA MATHEMATICA UPPSALA, 1966, 115 (3-4): : 271 - +
[49] On some exact solutions of non-linear elliptic equations system
Markov, YA
Markova, MA
DOKLADY AKADEMII NAUK, 1996, 346 (05) : 597 - 599
[50] MAXIMUM PRINCIPLE FOR NON-LINEAR PARABOLIC AND ELLIPTIC-EQUATIONS
KRYLOV, NV
MATHEMATICS OF THE USSR-IZVESTIYA, 1979, 13 (02): : 335 - 347

← 1 2 3 4 5 →