## 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 W^{1,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 |

卷 | 79 |

發行號 | 3 |

DOIs | |

出版狀態 | 已發佈 - 2021 九月 |

對外發佈 | 是 |

## ASJC Scopus subject areas

- 應用數學