Uniqueness of integrable solutions to first order systems with integrable tensor-coefficients and applications to elasticity

Abstract

For a Lipschitz domain we show that solutions of certain first order systems are unique. This result is then applied to prove a crucial step for showing Korn's first inequality as well as to prove the 'infinitesimal rigid displacement lemma in curvilinear coordinates'.

References in corpus (2)

• Maxwell meets Korn: A New Coercive Inequality for Tensor Fields with Square-Integrable Exterior Derivative
• A Canonical Extension of Korn's First Inequality to H(Curl) motivated by Gradient Plasticity with Plastic Spin

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• The exponentiated Hencky-logarithmic strain energy. Part III: Coupling with idealized isotropic finite strain plasticity
• $L^p$-trace-free generalized Korn inequalities for incompatible tensor fields in three space dimensions
• Derivation of a von Kármán plate theory for thermoviscoelastic solids