Minimum action solutions of some vector field equations

Haim Brezis, Elliott H. Lieb

Research output: Contribution to journalArticlepeer-review

115 Scopus citations

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/∂ui. Associated with this system is the action, S(u)=ε{1/2|∇u|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, v ≢0}.

Original languageEnglish (US)
Pages (from-to)97-113
Number of pages17
JournalCommunications In Mathematical Physics
Volume96
Issue number1
DOIs
StatePublished - Mar 1 1984

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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