Remarks on the theory of elasticity

Sergio Conti; Camillo de Lellis

Displaying similar documents to “Remarks on the theory of elasticity”

Topological degree, Jacobian determinants and relaxation

Irene Fonseca, Nicola Fusco, Paolo Marcellini (2005)

Bollettino dell'Unione Matematica Italiana

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A characterization of the total variation $T V (u, Ω)$ of the Jacobian determinant $det D u$ is obtained for some classes of functions $u : Ω \to R^{n}$ outside the traditional regularity space $W^{1, n} (Ω; R^{n})$ . In particular, explicit formulas are deduced for functions that are locally Lipschitz continuous away from a given one point singularity $x_{0} \in Ω$ . Relations between $T V (u, Ω)$ and the distributional determinant $Det D u$ are established, and an integral representation is obtained for the relaxed energy of certain polyconvex functionals at maps $u \in W^{1, p} (Ω; R^{n}) \cap W^{1, \infty} (Ω \{x_{0}\}; R^{n})$ . ...

On a new class of elastic deformations not allowing for cavitation

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Cartesian currents and variational problems for mappings into spheres

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Topological sectors for Ginzburg-Landau energies.

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Minimizers with topological singularities in two dimensional elasticity

Xiaodong Yan, Jonathan Bevan (2008)

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For a class of 2-D elastic energies we show that a radial equilibrium solution is the unique global minimizer in a subclass of all admissible maps. The boundary constraint is a double cover of $S^{1}$ ; the minimizer $u$ is $C^{1}$ and is such that $det \nabla u$ vanishes at one point.