Some vector field equations

Elliott H. Lieb

doi:10.1016/S0304-0208(08)73722-8

Some vector field equations

Elliott H. Lieb

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Systems of the type −Δu_i = gⁱ(u), with u = (u₁,…,u_n) and gⁱ(u) = ∂G/∂u_i on R^d, 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 language	English (US)
Pages (from-to)	403-412
Number of pages	10
Journal	North-Holland Mathematics Studies
Volume	92
Issue number	C
DOIs	https://doi.org/10.1016/S0304-0208(08)73722-8
State	Published - Jan 1 1984

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/S0304-0208(08)73722-8

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title = "Some vector field equations",

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.",

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N2 - 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.

AB - 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.

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U2 - 10.1016/S0304-0208(08)73722-8

DO - 10.1016/S0304-0208(08)73722-8

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JO - North-Holland Mathematics Studies

JF - North-Holland Mathematics Studies

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ER -

Some vector field equations

Abstract

All Science Journal Classification (ASJC) codes

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