Power Convexity of Solutions to a Special Lagrangian Equation in Dimension Two

被引：1

作者：

Zhang, Wei ^{[1
]}

Zhou, Qi ^{[1
]}

机构：

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou, Gansu, Peoples R China

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2023年 / 33卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Power convexity; Special Lagrangian equation; Constant rank theorem; CONSTANT RANK THEOREM; LEVEL SETS; ELLIPTIC PROBLEMS; DIRICHLET PROBLEM; BRUNN-MINKOWSKI; CONCAVITY; INEQUALITIES; EXISTENCE; DOMAINS; PHASES;

D O I：

10.1007/s12220-022-01186-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove power convexity result of solution to Dirichlet problem of special Lagrangian equation in dimension two. This provides new example of fully nonlinear elliptic boundary value problem whose solution shares power convexity property previously only knew for 2-Hessian equation in dimension three. The key ingredients consist of microscopic convexity principles and deformation methods.

引用

页数：13

共 49 条

[1] ON THE CONVEXITY OF LEVEL LINES OF THE FUNDAMENTAL MODE IN THE CLAMPED MEMBRANE PROBLEM, AND THE EXISTENCE OF CONVEX SOLUTIONS IN A RELATED FREE-BOUNDARY PROBLEM
ACKER, A
PAYNE, LE
PHILIPPIN, G
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1981, 32 (06): : 683 - 694
[2] Ahlfors L. V, 2010, CONFORMAL INVARIANTS
[3] Convex viscosity solutions and state constraints
Alvarez, O
Lasry, JM
Lions, PL
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1997, 76 (03): : 265 - 288
[4] Bhattacharya A, 2020, Arxiv, DOI arXiv:2005.14420
[5] A microscopic convexity principle for nonlinear partial differential equations
Bian, Baojun
Guan, Pengfei
[J]. INVENTIONES MATHEMATICAE, 2009, 177 (02) : 307 - 335
[6] Quasiconcave Solutions to Elliptic Problems in Convex Rings
Bianchini, Chiara
Longinetti, Marco
Salani, Paolo
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2009, 58 (04) : 1565 - 1589
[7] Bianchini M, 2013, SPRINGER INDAM SER, V2, P35, DOI 10.1007/978-88-470-2841-8_3
[8] Borrelli W., 2022, PREPRINT
[9] ON EXTENSIONS OF BRUNN-MINKOWSKI AND PREKOPA-LEINDLER THEOREMS, INCLUDING INEQUALITIES FOR LOG CONCAVE FUNCTIONS, AND WITH AN APPLICATION TO DIFFUSION EQUATION
BRASCAMP, HJ
LIEB, EH
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1976, 22 (04) : 366 - 389
[10] 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

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