A new approach to counterexamples to L estimates: Korn’s inequality, geometric rigidity, and regularity for gradients of separately convex functions
نویسندگان
چکیده
A new approach to counterexamples to A new approach to counterexamples to L The derivation of counterexamples to L 1 estimates can be reduced to a geometric decomposition procedure along rank-one lines in matrix space. We illustrate this concept in two concrete applications. Firstly, we recover a celebrated, and rather complex, counterexample by Ornstein, proving the failure of Korn's inequality, and of the corresponding geometrically nonlinear rigidity result, in L 1. Secondly, we construct a function f : R 2 → R which is separately convex but whose gradient is not in BV loc , in the sense that the mixed derivative ∂ 2 f /∂x 1 ∂x 2 is not a bounded measure.
منابع مشابه
A New Approach to Counterexamples to L1 Estimates: Korn’s Inequality, Geometric Rigidity, and Regularity for Gradients of Separately Convex Functions
The derivation of counterexamples to L1 estimates can be reduced to a geometric decomposition procedure along rank-one lines in matrix space. We illustrate this concept in two concrete applications. Firstly, we recover a celebrated, and rather complex, counterexample by Ornstein, proving the failure of Korn’s inequality, and of the corresponding geometrically nonlinear rigidity result, in L1. S...
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