Conservation laws for fourth order systems in four dimensions

被引：59

作者：

Lamm, Tobias ^{[1
]}

Riviere, Tristan ^{[1
]}

机构：

[1] ETH, Dept Math, CH-8092 Zurich, Switzerland

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2008年 / 33卷 / 02期

关键词：

biharmonic map heat flow; conservation laws; fourth order elliptic systems; lorentz spaces; wente inequality;

D O I：

10.1080/03605300701382381

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Following an approach of the second author (Rivire, 2007) for conformally invariant variational problems in two dimensions, we show in four dimensions the existence of a conservation law for fourth order systems, which includes both intrinsic and extrinsic biharmonic maps. With the help of this conservation law we prove the continuity of weak solutions of this system. Moreover we use the conservation law to derive the existence of a unique global weak solution of the extrinsic biharmonic map flow in the energy space.

引用

页码：245 / 262

页数：18

共 28 条

[1] MULTIPLE SOLUTIONS OF H-SYSTEMS AND RELLICH CONJECTURE
BREZIS, H
CORON, JM
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1984, 37 (02) : 149 - 187
[2] Chang SYA, 1999, COMMUN PUR APPL MATH, V52, P1113, DOI 10.1002/(SICI)1097-0312(199909)52:9<1113::AID-CPA4>3.0.CO
[3] 2-7
[4] COIFMAN R, 1993, J MATH PURE APPL, V72, P247
[5] DISCONTINUOUS SOLUTION OF A MILDLY NONLINEAR ELLIPTIC SYSTEM
FREHSE, J
[J]. MATHEMATISCHE ZEITSCHRIFT, 1973, 134 (03) : 229 - 230
[6] FREIRE A, 1995, CALC VAR PARTIAL DIF, V3, P95, DOI 10.1007/BF01190893
[7] Uniqueness for the harmonic map flow from surfaces to general targets (vol 70, pg 310, 1995)
Freire, A
[J]. COMMENTARII MATHEMATICI HELVETICI, 1996, 71 (02) : 330 - 337
[8] UNIQUENESS FOR THE HARMONIC MAP FLOW FROM SURFACES TO GENERAL TARGETS
FREIRE, A
[J]. COMMENTARII MATHEMATICI HELVETICI, 1995, 70 (02) : 310 - 338
[9] The extrinsic polyharmonic map heat flow in the critical dimension
Gastel, Andreas
[J]. ADVANCES IN GEOMETRY, 2006, 6 (04) : 501 - 521
[10] Helein F., 2002, HARMONIC MAPS CONSER, V150

← 1 2 3 →