Existence and uniqueness solution of Euler-Lagrange equation in Sobolev space W^{1,p}(\Omega) with Gateaux derivative

Christyanti, Ratna Dwi; Wibowo, Ratno Bagus Edy; Alghofari, Abdul Rouf

doi:10.12988/ijma.2014.45138

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2021

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“…Christyanti and Wibowo [10] discussed the existence and uniqueness of solutions u of the Euler-Lagrange equation in Sobolev space W 1,p , with Gateaux derivative, for a functional of form…”

Section: Introductionmentioning

confidence: 99%

Composition functionals in higher order calculus of variations and Noether's theorem

Frederico

Sousa

Almeida

2021

Applicable Analysis

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In the present paper we discuss the existence and uniqueness of solution for higherorder calculus of variations problems, involving composition of functionals. Also, higher-order DuBois-Reymond conditions in the Sobolev space W m,p ([t1, t2]; R) are proven, both in integral and differential form, and under additional constraints. We consider the higher-order Noether's theorem and discuss invariance conditions for the main problem.

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“…Christyanti and Wibowo [10] discussed the existence and uniqueness of solutions u of the Euler-Lagrange equation in Sobolev space W 1,p , with Gateaux derivative, for a functional of form…”

Section: Introductionmentioning

confidence: 99%