### Abstract

Let A_{1}(x, D) and A_{2}(x, D) be differential operators of the first order acting on l-vector functions u = (u^{1}, . . . , u^{1}) in a bounded domain Ω ⊂ ℝ^{n} with the smooth boundary ∂Ω. We assume that the H^{1}-norm, is equivalent to, where B_{i} = B_{i}(x, ν) is the trace operator onto ∂ Ω associated with A_{i}(x, D) for i = 1, 2 which is determined by the Stokes integral formula (ν: unit outer normal to ∂Ω. Furthermore, we impose on A_{1} and A_{2} a cancellation property such as A_{1}A_{2}′ = 0 and A_{2}A_{1}′ = 0, where A_{i}′ is the formal adjoint differential operator of A_{i}(i = 1, 2). Suppose that and converge to u and v weakly in L^{2}(Ω), respectively. Assume also that and are bounded in L^{2}(Ω). If either or is bounded in H^{1/2}(∂Ω), then it holds that. We also discuss a corresponding result on compact Riemannian manifolds with boundary.

Original language | English |
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Pages (from-to) | 879-905 |

Number of pages | 27 |

Journal | Archive for Rational Mechanics and Analysis |

Volume | 207 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2013 Jan 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering

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## Cite this

*Archive for Rational Mechanics and Analysis*,

*207*(3), 879-905. https://doi.org/10.1007/s00205-012-0583-7