اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the optimal constants in Korns and geometric rigidity estimates, in bounded and unbounded domains, under Neumann boundary conditions
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We are concerned with the optimal constants: in the Korn inequality under tangential boundary conditions on bounded sets $Omega subset mathbb{R}^n$, and in the geometric rigidity estimate on the whole $mathbb{R}^2$. We prove that the latter constant equals $sqrt{2}$, and we discuss the relation of the former constants with the optimal Korns constants under Dirichlet boundary conditions, and in the whole $mathbb{R}^n$, which are well known to equal $sqrt{2}$. We also discuss the attainability of these constants and the structure of deformations/displacement fields in the optimal sets.
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