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

Research output: Contribution to journal › Research article › Contributed › peer-review

Contributors

  • Johannes Lankeit - , University of Duisburg-Essen (Author)
  • Patrizio Neff - , University of Duisburg-Essen (Author)
  • Dirk Pauly - , Institute of Analysis, University of Duisburg-Essen (Author)

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).

Details

Original languageEnglish
Pages (from-to)1679-1688
Number of pages10
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume64
Issue number6
Publication statusPublished - Dec 2013
Peer-reviewedYes

External IDs

ORCID /0000-0003-4155-7297/work/145224247

Keywords

ASJC Scopus subject areas

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