منابع مشابه
The Uniform Korn - Poincaré Inequality in Thin Domains L’inégalité De Korn - Poincaré Dans Les Domaines Minces
We study the Korn-Poincaré inequality: ‖u‖W1,2(Sh) ≤ Ch‖D(u)‖L2(Sh), in domains S that are shells of small thickness of order h, around an arbitrary compact, boundaryless and smooth hypersurface S in R. By D(u) we denote the symmetric part of the gradient ∇u, and we assume the tangential boundary conditions: u · ~n = 0 on ∂S. We prove that Ch remains uniformly bounded as h→ 0, for vector fields...
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A quadratic inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be applied to the study of global existence of solutions to nonlinear PDE.
متن کاملThe Uniform Korn - Poincaré Inequality in Thin Domains
We study the Korn-Poincaré inequality: ‖u‖ W1,2(Sh) ≤ Ch‖D(u)‖L2(Sh), in domains S that are shells of small thickness of order h, around an arbitrary smooth and closed hypersurface S in R. By D(u) we denote the symmetric part of the gradient ∇u, and we assume the tangential boundary conditions: u · ~n = 0 on ∂S. We prove that Ch remains uniformly bounded as h → 0, for vector fields u in any fam...
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ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2006
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2005.10.010