Analytic characterization of monotone Hopf-harmonics

被引：0
作者：
Kangasniemi, Ilmari [1 ]
Koski, Aleksis [2 ]
Onninen, Jani [1 ,3 ]
机构：
[1] Syracuse Univ, Dept Math, Syracuse, NY 13244 USA
[2] Univ Helsinki, Dept Math & Stat, POB 68 Pietari Kalmin Katu 5, Helsinki 00014, Finland
[3] Univ Jyvaskyla, Dept Math & Stat, POB 35 MaD, Jyvaskyla 40014, Finland
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2022年 / 61卷 / 04期
基金：
芬兰科学院;
关键词：
Primary; 31C45; Secondary; 35J25; 58E20; 74B20; 46E35; GLOBAL INVERTIBILITY; MAPPINGS; DEFORMATIONS; REGULARITY; EQUATION; THEOREM;
D O I：
10.1007/s00526-022-02246-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study solutions of the inner-variational equation associated with the Dirichlet energy in the plane, given homeomorphic Sobolev boundary data. We prove that such a solution is monotone if and only if its Jacobian determinant does not change sign. These solutions, called monotone Hopf-harmonics, are a natural alternative to harmonic homeomorphisms. Examining the topological behavior of a solution (not a priori monotone) on the trajectories of Hopf quadratic differentials plays a sizable role in our arguments.
引用
收藏
页数：25
相关论文
共 44 条
[11]  
Brezis H., 1996, SELECTA MATH, V2, P309
[12]  
Choquet G., 1945, B SCI MATH, V89, P156
[13]  
Ciarlet P.G, 1988, STUDIES MATH APPLICA, V20
[14]  
Cristina J, 2014, ANN SCUOLA NORM-SCI, V13, P1145
[15]   Solution of the problem of plateau [J].
Douglas, Jesse .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1931, 33 (1-4) :263-321
[16]  
Engelking R., 1989, GEN TOPOLOGY
[17]  
Garabedian PR., 1953, J ANAL MATH, V2, P281, DOI [10.1007/BF02825640, DOI 10.1007/BF02825640]
[18]   A WEAK APPROACH TO FINITE ELASTICITY [J].
GIAQUINTA, M ;
MODICA, G ;
SOUCEK, J .
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 1994, 2 (01) :65-100
[19]  
Heinonen J., 2006, NONLINEAR POTENTIAL
[20]  
Hencl S, 2014, LECT NOTES MATH, V2096, P1, DOI 10.1007/978-3-319-03173-6
12345