L^p -trace-free version of the generalized Korn inequality for incompatible tensor fields in arbitrary dimensions - Archive ouverte HAL Access content directly
Journal Articles Zeitschrift für Angewandte Mathematik und Physik Year : 2021

L^p -trace-free version of the generalized Korn inequality for incompatible tensor fields in arbitrary dimensions

Abstract

For n ≥ 3 and 1 < p < ∞ we prove an L^p-version of the generalized trace-free Korn-type inequality for incompatible, p-integrable tensor fields P : Ω → R^(n×n) having p-integrable generalized Curl_n and generalized vanishing tangential trace, more precisely there exists a constant c = c(n, p, Ω) such that |P|_(L^p) ≤ c (|dev_n sym P|_(L^p) + |Curl_n P|_(L^p), where the generalized Curl_n is given by (Curl_n P)_{ijk} := ∂_iP_{kj} − ∂_jP_{ki} and dev_n X := X − 1_n tr(X) · id denotes the deviatoric (trace-free) part of the square matrix X. The improvement towards the three-dimensional case comes from a novel matrix representation of the generalized cross product.
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Dates and versions

hal-02967603 , version 1 (15-10-2020)
hal-02967603 , version 2 (25-05-2021)

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Cite

Peter Lewintan, Patrizio Neff. L^p -trace-free version of the generalized Korn inequality for incompatible tensor fields in arbitrary dimensions. Zeitschrift für Angewandte Mathematik und Physik, 2021, 72 (3), ⟨10.1007/s00033-021-01550-6⟩. ⟨hal-02967603v2⟩

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