A New Approach to Counterexamples to L1 Estimates: Korn’s Inequality, Geometric Rigidity, and Regularity for Gradients of Separately Convex Functions
نویسندگان
چکیده
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. Secondly, we construct a function f : R2 −→ R which is separately convex but whose gradient is not in BVloc, in the sense that the mixed derivative ∂f/∂x1∂x2 is not a bounded measure.
منابع مشابه
A new approach to counterexamples to L estimates: Korn’s inequality, geometric rigidity, and regularity for gradients of separately convex functions
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 inequalit...
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