## Abstract

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)).

Original language | English |
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Pages (from-to) | 409-417 |

Number of pages | 9 |

Journal | Quarterly of Applied Mathematics |

Volume | 79 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2021 Sep |

Externally published | Yes |

## Keywords

- BMO local minimizers
- Bounded mean oscillation
- Taylor’s theorem

## ASJC Scopus subject areas

- Applied Mathematics