Local regularity for concave homogeneous complex degenerate elliptic equations dominating the Monge-Ampere equation

被引：4

作者：

Abja, Soufian ^{[1
]}

Olive, Guillaume ^{[1
]}

机构：

[1] Jagiellonian Univ, Fac Math & Comp Sci, Ul Lojasiewicza 6, PL-30348 Krakow, Poland

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2022年 / 201卷 / 02期

关键词：

Degenerate elliptic equations; Local regularity; Hessian equations; DIRICHLET PROBLEM; DUALITY;

D O I：

10.1007/s10231-021-01129-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish a local regularity result for W-loc(2,p) solutions to complex degenerate nonlinear elliptic equations F(D(C)(2)u) = f when they dominate the Monge-Ampere equation. Notably, we apply our result to the so-called k-Monge-Ampere equation.

引用

页码：561 / 587

页数：27

共 50 条

[41] ON THE REGULARITY PROBLEM OF COMPLEX MONGE-AMPERE EQUATIONS WITH CONICAL SINGULARITIES
Chen, Xiuxiong
Wang, Yuanqi
ANNALES DE L INSTITUT FOURIER, 2017, 67 (03) : 969 - 1003
[42] ON THE C2,α-REGULARITY OF THE COMPLEX MONGE-AMPERE EQUATION
Wang, Yu
MATHEMATICAL RESEARCH LETTERS, 2012, 19 (04) : 939 - 946
[43] C1,1 regularity for degenerate complex Monge-Ampere equations and geodesic rays
Chu, Jianchun
Tosatti, Valentino
Weinkove, Ben
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2018, 43 (02) : 292 - 312
[44] A Priori L∞-Estimates for Degenerate Complex Monge-Ampere Equations
Eyssidieux, Philippe
Guedj, Vincent
Zeriahi, Ahmed
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2008, 2008
[45] The complex Monge-Ampere equation
Kolodziej, S
ACTA MATHEMATICA, 1998, 180 (01) : 69 - 117
[46] Complex Monge-Ampere Equations
Phong, D. H.
Song, Jian
Sturm, Jacob
IN MEMORY OF C.C. HSIUNG: LECTURES GIVEN AT THE JDG SYMPOSIUM, LEHIGH UNIVERSITY, JUNE 2010, 2012, 17 : 327 - +
[47] REGULARITY OF GENERALIZED SOLUTIONS OF MONGE-AMPERE EQUATIONS
URBAS, JIE
MATHEMATISCHE ZEITSCHRIFT, 1988, 197 (03) : 365 - 393
[48] Regularity of degenerate Monge-Ampere and prescribed Gaussian curvature equations in two dimensions
Sawyer, ET
Wheeden, RL
POTENTIAL ANALYSIS, 2006, 24 (03) : 267 - 301
[49] THE DEGENERATE MONGE-AMPERE EQUATIONS WITH THE NEUMANN CONDITION
Shi, Juhua
Jiang, Feida
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2021, 20 (02) : 915 - 931
[50] Regularity of weak solutions to the Monge-Ampere equation
Gutiérrez, CE
Hartenstine, D
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 355 (06) : 2477 - 2500

← 1 2 3 4 5 →