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Erschienen in:
2002 | OriginalPaper | Buchkapitel
Minimum Action Solutions of Some Vector Field Equations
verfasst von : Haim Brezis, Elliott H. Lieb
Erschienen in: Inequalities
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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The system of equations studied in this paper is— Δui = gi(u) on Rd, d≧ 2, with u:Rd-→]Rn and gi(u)=∂G/∂i. Associated with this system is the action, S(u) = f {1/2|2 — G(u)}. Under appropriate conditions on G (which differ for d = 2 and d≧ 3) 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, u0}.