Displaying similar documents to “General and physically privileged solutions to certain symmetric systems of linear P.D.E.s with tensor functionals as unknowns”

On tensor functions whose gradients have some skew-symmetries

Adriano Montanaro (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let V n be a real inner product space of any dimension; and let Q α 1 ⁢ … ⁢ α v = Q ⌃ α 1 ⁢ … ⁢ α v ⁢ X β ⁢ 1 ⁢ … ⁢ β τ be a C 2 -map relating any two tensor spaces on V n . We study the consequences imposed on the form of this function by the condition that its gradient should be skew-symmetric with respect to some pairs α μ , β η of indexes. Any such a condition is written as a system of linear partial differential equations, with constant coefficients, which is symmetric with respect to certain couples of independent variables. The solutions of these...

Invariant line integrals in the theory of defective crystals

Gareth P. Parry, Miroslav Šilhavý (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In a continuum theory of crystals with defects, invariant line integrals measure the line defects of the lattice structure. It is shown that the integrands of invariant line integrals can always be taken to have the transformation properties of covariant vector-valued functions.

Conical differentiability for bone remodeling contact rod models

Isabel N. Figueiredo, Carlos F. Leal, Cecília S. Pinto (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove the conical differentiability of the solution to a bone remodeling contact rod model, for given data (applied loads and rigid obstacle), with respect to small perturbations of the cross section of the rod. The proof is based on the special structure of the model, composed of a variational inequality coupled with an ordinary differential equation with respect to time. This structure enables the verification of the two following fundamental results: the polyhedricity of a modified...