After introducing the concept of functional dissipativity of the Dirichlet problem in a domain $\Omega\subset R^N$ for systems of partial differential operators of the form $\partial_{x_h}(A_{hk}(x)/\partial_{x_k}), $\{A_{hk}\}$ being $mxm$ matrices with complex valued $L^\infty$ entries), we find necessary and sufficient conditions for the functional dissipativity of the two-dimensional Lamé system. As an application of our theory we provide two regularity results for the displacement vector in the N-dimensional equilibrium problem, when the body is fixed along its boundary.
Criterion for the functional dissipativity of the Lamé operator
Cialdea A.;
2023-01-01
Abstract
After introducing the concept of functional dissipativity of the Dirichlet problem in a domain $\Omega\subset R^N$ for systems of partial differential operators of the form $\partial_{x_h}(A_{hk}(x)/\partial_{x_k}), $\{A_{hk}\}$ being $mxm$ matrices with complex valued $L^\infty$ entries), we find necessary and sufficient conditions for the functional dissipativity of the two-dimensional Lamé system. As an application of our theory we provide two regularity results for the displacement vector in the N-dimensional equilibrium problem, when the body is fixed along its boundary.File in questo prodotto:
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