Minimum Action Solutions of Some Vector Field Equations

Haim Brezis and Elliott H. Lieb
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Haim Brezis: Université Paris VI, Département de Mathématiques
Elliott H. Lieb: Princeton University, Departments of Mathematics and Physics

A chapter in Inequalities, 2002, pp 563-579 from Springer

Abstract: Abstract 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}.

Keywords: Compact Support; Radial Solution; Riesz Representation Theorem; Schrodinger Operator; Elliptic Regularity Theory (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-55925-9_45

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DOI: 10.1007/978-3-642-55925-9_45

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