Regularity of Solutions to the Dirichlet Problem for Monge-Ampere Equations

被引：1

作者：

Charabati, Mohamad ^{[1
]}

机构：

[1] Univ Paul Sabatier, Inst Math Toulouse, 118 Route Narbonne, F-31062 Toulouse 09, France

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2017年 / 66卷 / 06期

关键词：

Complex Monge-Ampere equation; Hausdorff-Riesz measure; strongly hyperconvex Lipschitz domain; plurisubharmonic function; HOLDER CONTINUOUS SOLUTIONS; CONTINUITY;

D O I：

10.1512/iumj.2017.66.6190

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study Holder continuity of solutions to the Dirichlet problem for measures having density in L-p, p > 1 with respect to Hausdorff-Riesz measures of order 2n - 2 + epsilon for 0 < epsilon <= 2, in a bounded strongly hyperconvex Lipschitz domain. We note that the boundary data belongs to C-0,C-alpha (partial derivative Omega), 0 < alpha <= 1.

引用

页码：2187 / 2204

页数：18

共 50 条

[41] C1,α REGULARITY OF SOLUTIONS TO PARABOLIC MONGE-AMPERE EQUATIONS
Daskalopoulos, Panagiota
Savin, Ovidiu
AMERICAN JOURNAL OF MATHEMATICS, 2012, 134 (04) : 1051 - 1087
[42] Regularity estimates of solutions to complex Monge-Ampere equations on Hermitian manifolds
Zhang, Xi
Zhang, Xiangwen
JOURNAL OF FUNCTIONAL ANALYSIS, 2011, 260 (07) : 2004 - 2026
[43] DIRICHLET PROBLEM FOR A COMPLEX MONGE-AMPERE EQUATION
BEDFORD, E
TAYLOR, BA
INVENTIONES MATHEMATICAE, 1976, 37 (01) : 1 - 44
[44] ON THE DIRICHLET PROBLEM FOR THE COMPLEX MONGE-AMPERE OPERATOR
LEVENBERG, N
OKADA, M
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1991, 313 (11): : 747 - 750
[45] DIRICHLET PROBLEM FOR MONGE-AMPERE EQUATIONS AND THEIR N-DIMENSIONAL ANALOGUES
BAKELMAN, IJ
DOKLADY AKADEMII NAUK SSSR, 1959, 126 (05): : 923 - 926
[46] Dirichlet problem for relative real Monge-Ampere equations on Riemann functions
Atallah, A
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1996, 21 (1-2) : 35 - 62
[47] ON THE DIRICHLET PROBLEM FOR THE COMPLEX MONGE-AMPERE OPERATOR
LEVENBERG, N
OKADA, M
MICHIGAN MATHEMATICAL JOURNAL, 1993, 40 (03) : 507 - 526
[48] ON THE DIRICHLET PROBLEM FOR THE COMPLEX MONGE-AMPERE OPERATOR
CEGRELL, U
MATHEMATISCHE ZEITSCHRIFT, 1984, 185 (02) : 247 - 251
[49] On radial solutions for Monge-Ampere equations
Liu, Ronghua
Wang, Fanglei
An, Yukun
TURKISH JOURNAL OF MATHEMATICS, 2018, 42 (04) : 1590 - 1609
[50] Regularity of Solutions to the Quaternionic Monge-Ampere Equation
Kolodziej, Slawomir
Sroka, Marcin
JOURNAL OF GEOMETRIC ANALYSIS, 2020, 30 (03) : 2852 - 2864

← 1 2 3 4 5 →