Minimum action solutions of some vector field equations

Haim Brezis, Elliott H. Lieb

Research output: Contribution to journalArticlepeer-review

133 Scopus citations


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
Issue number1
StatePublished - Mar 1984

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


Dive into the research topics of 'Minimum action solutions of some vector field equations'. Together they form a unique fingerprint.

Cite this