Why bootstrapping for J-holomorphic curves fails in Ck

被引：0

作者：

Geiges, Hansjoerg ^{[1
]}

Saglam, Murat ^{[1
]}

Zehmisch, Kai ^{[2
]}

机构：

[1] Univ Cologne, Math Inst, Weyertal 86-90, D-50931 Cologne, Germany

[2] Ruhr Univ Bochum, Fak Math, Univ Str 150, D-44780 Bochum, Germany

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2023年 / 13卷 / 01期

关键词：

Elliptic bootstrapping; Calderon-Zygmund estimate; (partial derivative)over-bar-operator; Pseudoholomorphic curve;

D O I：

10.1007/s13324-022-00775-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a simple example for the failure of the Calderon-Zygmund estimate for the (partial derivative) over bar -operator when the Sobolev (k, p)-norms are replaced by the C-k-norms. This example is discussed in the context of elliptic bootstrapping, Fredholm theory, and the regularity of J-holomorphic curves.

引用

页数：11

共 50 条

[1] Singularities of J-holomorphic curves
Sikorav, JC
[J]. MATHEMATISCHE ZEITSCHRIFT, 1997, 226 (03) : 359 - 373
[2] Approximating J-holomorphic curves by holomorphic ones
Rivière, T
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2004, 21 (03) : 273 - 285
[3] Approximating J-holomorphic curves by holomorphic ones
Tristan Riviére
[J]. Calculus of Variations and Partial Differential Equations, 2004, 21 : 273 - 285
[4] J-Holomorphic Curves in a Nef Class
Li, Tian-Jun
Zhang, Weiyi
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2015, 2015 (22) : 12070 - 12104
[5] Relative frames on J-holomorphic curves
Lazzarini, Laurent
[J]. JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2011, 9 (02) : 213 - 256
[6] Relative frames on J-holomorphic curves
Laurent Lazzarini
[J]. Journal of Fixed Point Theory and Applications, 2011, 9 : 213 - 256
[7] J-holomorphic curves and symplectic invariants
Lalonde, F
[J]. GAUGE THEORY AND SYMPLECTIC GEOMETRY, 1997, 488 : 147 - 174
[8] A variational characterization of J-holomorphic curves
Arezzo, Claudio
Sun, Jun
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2015, 709 : 171 - 200
[9] A reverse isoperimetric inequality for J-holomorphic curves
Groman, Yoel
Solomon, Jake P.
[J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2014, 24 (05) : 1448 - 1515
[10] Nongeneric J-holomorphic curves and singular inflation
McDuff, Dusa
Opshtein, Emmanuel
[J]. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2015, 15 (01): : 231 - 286

← 1 2 3 4 5 →