Taylor’s Theorem for Functionals on BMO With Application to BMO Local Minimizers

Daniel E. Spector*, Scott J. Spector

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

1 引文 斯高帕斯(Scopus)

摘要

In this note two results are established for energy functionals that are given by the integral of W(x, ∇u(x)) over Ω ⊂ (Formula presented) with ∇u ∈ BMO(Ω; (Formula presented)), the space of functions of Bounded Mean Oscillation of John and Nirenberg. A version of Taylor’s theorem is first shown to be valid provided the integrand W has polynomial growth. This result is then used to demonstrate that every Lipschitz-continuous solution of the corre-sponding Euler-Lagrange equations at which the second variation of the energy is uni-formly positive is a strict local minimizer of the energy in W1,BMO(Ω; (Formula presented) ), the subspace of the Sobolev space W1,1(Ω; (Formula presented) ) for which the weak derivative ∇u ∈ BMO(Ω; (Formula presented)).

原文英語
頁(從 - 到)409-417
頁數9
期刊Quarterly of Applied Mathematics
79
發行號3
DOIs
出版狀態已發佈 - 2021 九月
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ASJC Scopus subject areas

  • 應用數學

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