Static Elasticity in a Riemannian Manifold

DOI10.1007/978-3-319-18573-6_11zbMath1325.74025OpenAlexW2241740843MaRDI QIDQ3449744

Christinel Mardare

Publication date: 5 November 2015

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://hal.sorbonne-universite.fr/hal-01083499/file/ElasticityRiemannManifold.pdf

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Applications of differential geometry to physics (53Z05) Applications of global differential geometry to the sciences (53C80)

Related Items (1)

Layer potentials and Poisson problems for the nonsmooth coefficient Brinkman system in Sobolev and Besov spaces

Cites Work

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• The equations of elastostatics in a Riemannian manifold
• On local and global existence of Killing vector-fields
• Elastic theory of unconstrained non-Euclidean plates
• Manifolds, tensor analysis, and applications.
• Cauchy's theorem on manifolds
• The geometry of Cauchy's fluxes
• A Riemannian version of Korn's inequality
• On the motion of a compact elastic body
• ON THE NEWTON–KANTOROVICH THEOREM
• Static self-gravitating elastic bodies in Einstein gravity
• Applications of Estimates near the Boundary to Regularity of Solutions in Linearized Elasticity
• Forces and the existence of stresses in invariant continuum mechanics
• Differentiable manifolds and the principle of virtual work in continuum mechanics
• Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension
• Static, self–gravitating elastic bodies
• Relativistic elasticity
• Relativistic elastostatics: I. Bodies in rigid rotation
• Foundations of general relativistic high-pressure elasticity theory
• A correction of an inconsistency in my paper ``Cauchy's theorem on manifolds

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