Divergence measure fields and Cauchy's stress theorem

zbMath1167.74317MaRDI QIDQ2504938

Šilhavý, Miroslav

Publication date: 28 September 2006

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/108654

Mathematics Subject Classification ID

Stress (74A10)

Related Items (25)

On BV functions and essentially bounded divergence-measure fields in metric spaces ⋮ The Hardy-Morrey \& Hardy-John-Nirenberg inequalities involving distance to the boundary ⋮ A note on equilibrated stress fields for no-tension bodies under gravity ⋮ On locally essentially bounded divergence measure fields and sets of locally finite perimeter ⋮ Anisotropic tubular neighborhoods of sets ⋮ A new mathematical foundation for contact interactions in continuum physics ⋮ Representation formulas for pairings between divergence-measure fields and \(BV\) functions ⋮ Eigenvalue problems in 𝐿^{∞}: optimality conditions, duality, and relations with optimal transport ⋮ Extensions and traces of BV functions in rough domains and generalized Cheeger sets ⋮ Fine properties of symmetric and positive matrix fields with bounded divergence ⋮ Traces and extensions of bounded divergence-measure fields on rough open sets ⋮ A version of Stokes's theorem using test curves ⋮ Regularity of fluxes in nonlinear hyperbolic balance laws ⋮ Anzellotti's pairing theory and the Gauss-Green theorem ⋮ Description of limiting vorticities for the magnetic 2D Ginzburg-Landau equations ⋮ Cauchy fluxes and Gauss-Green formulas for divergence-measure fields over general open sets ⋮ Occupational measures and averaged shape optimization ⋮ The Gauss-Green theorem in stratified groups ⋮ Rough traces of BV functions in metric measure spaces ⋮ Back to the roots of vector and tensor calculus: Heaviside versus Gibbs ⋮ Removable singularities for div v=f in weighted Lebesgue spaces ⋮ Cauchy's stress theorem for stresses represented by measures ⋮ A phase-field approach to Eulerian interfacial energies ⋮ Pairings between bounded divergence-measure vector fields and BV functions ⋮ Area theorem and smoothness of compact Cauchy horizons

Cites Work

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• Pairings between measures and bounded functions and compensated compactness
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• A variational proof of the stress theorem of Cauchy
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• Cauchy's stress theorem and tensor fields with divergences in \(L^ p\)
• Cauchy's theorem in classical physics
• The principle of virtual work and integral laws of motion
• Divergence-measure fields and hyperbolic conservation laws
• Cauchy fluxes associated with tensor fields having divergence measure
• Balanced powers in continuum mechanics
• Extended divergence-measure fields and the Euler equations for gas dynamics
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• The geometry of Cauchy's fluxes
• The Cauchy Stress Theorem for bodies with finite perimeter
• On the theory of divergence-measure fields and its applications
• ON THE MEASURE-THEORETIC FOUNDATIONS OF THE SECOND LAW OF THERMODYNAMICS
• Decomposition and integral representation of Cauchy interactions associated with measures
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