Some vector field equations

Elliott H. Lieb

Research output: Contribution to journalArticlepeer-review

Abstract

Systems of the type −Δui = gi(u), with u = (u1,…,un) and gi(u) = ∂G/∂ui on Rd, d ≥ 2 are studied. Under suitable conditions on G and g it is shown that there is a solution of the system that also minimizes the action, S(u) = ∫|∇u|2 − ∫G(u) within the class of all nontrivial finite action solutions of the system.

Original languageEnglish (US)
Pages (from-to)403-412
Number of pages10
JournalNorth-Holland Mathematics Studies
Volume92
Issue numberC
DOIs
StatePublished - Jan 1 1984

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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