Uniqueness of integrable solutions to ∇ ζ=G ζ, ζǀGamma = 0 for integrable tensor coefficients G and applications to elasticity

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Johannes Lankeit
  • Patrizio Neff
  • Dirk Pauly

External Research Organisations

  • University of Duisburg-Essen
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Details

Original languageEnglish
Pages (from-to)1679-1688
Number of pages10
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume64
Publication statusPublished - 28 Feb 2013
Externally publishedYes

Abstract

Let Ω ⊂ ℝN be a Lipschitz domain and Γ be a relatively open and non-empty subset of its boundary ∂Ω. We show that the solution to the linear first-order system (Formula is Presented) is unique if (Formula is Presented) and (Formula is Presented). As a consequence, we prove (Formula is Presented) to be a norm for (Formula is Presented) for some p, q > 1 with 1/p + 1/q = 1 as well as det (Formula is Presented). We also give a new and different proof for the so-called 'infinitesimal rigid displacement lemma' in curvilinear coordinates: Let (Formula is Presented) satisfy sym (Formula is Presented) for some (Formula is Presented). Then, there exist a constant translation vector (Formula is Presented).

Keywords

    First-order system of partial differential equations, Generalized Korn's first inequality, Infinitesimal rigid displacement lemma, Korn's inequality, Korn's inequality in curvilinear coordinates, Unique continuation, Uniqueness

ASJC Scopus subject areas

Cite this

Uniqueness of integrable solutions to ∇ ζ=G ζ, ζǀGamma = 0 for integrable tensor coefficients G and applications to elasticity. / Lankeit, Johannes; Neff, Patrizio; Pauly, Dirk.
In: Zeitschrift fur Angewandte Mathematik und Physik, Vol. 64, 28.02.2013, p. 1679-1688.

Research output: Contribution to journal › Article › Research › peer review

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AU - Lankeit, Johannes

AU - Neff, Patrizio

AU - Pauly, Dirk

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