Minimum action solutions of some vector field equations |
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| Authors: | Haim Brezis Elliott H Lieb |
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| Institution: | (1) Département de Mathématiques, Université Paris VI, 4, Place Jussieu, F-75230 Paris, Cédex 05, France;(2) Departments of Mathematics and Physics, Princeton University, P.O. Box 708, 08544 Princeton, NJ, USA |
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| Abstract: | The system of equations studied in this paper is – u
i
=g
i
(u) on 
d
,d 2, withu:
d
n
andg
i
(u)= G/u
i
. Associated with this system is the action,S(u)= {1/2| u|2–G(u)}. Under appropriate conditions onG (which differ ford=2 andd3) it is proved that the system has a solution,u  0, of finite action and that this solution also minimizes the action within the class {v is a solution,v has finite action,v 0}.Work partially supported by U.S. National Science Foundation Grant PHY-81-16101-A02 |
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| Keywords: | |
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