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We employ partly Sobolev classes to obtain a necessary condition for mappings of $$W^{1,p}$$ W 1 , p -class to be deformations of nonlinearly elastic bodies that can be induced by $$L^{q}$$ L q -forces, $$1\le p,\,q <\infty $$ 1 ≤ p , q < ∞ . This condition is useful for studying continuous deformations of non-homogeneous materials and for obtaining stable numerical methods for nonlinear elasticity.
Zeitschrift für angewandte Mathematik und Physik – Springer Journals
Published: Nov 29, 2017
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