Abstract
Abstract
We show that, in order to decide whether a given probability measure is laminate, it is enough to verify Jensen’s inequality in the class of extremal non-negative rank-one convex integrands. We also identify a subclass of these extremal integrands, consisting of truncated minors, thus proving a conjecture made by Šverák (Arch Ration Mech Anal 119(4):293–300, 1992).
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference46 articles.
1. Astala, K., Iwaniec, T., Martin, G.: Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48). Princeton University Press, Princeton (2009)
2. Astala, K., Iwaniec, T., Prause, I., Saksman, E.: Burkholder integrals, Morrey’s problem and quasiconformal mappings. J. Am. Math. Soc. 25(2), 507–531 (2012)
3. Astala, K., Iwaniec, T., Prause, I., Saksman, E.: A hunt for sharp $$L^p$$-estimates and rank-one convex variational integrals. Filomat 29(2), 245–261 (2015)
4. Baernstein, A., Montgomery-Smith, S.J.: Some conjectures about integral means of $$\partial f$$ and $${\bar{\partial }} f$$. Complex analysis and differential equations (Uppsala, 1997). Acta Univ. Ups. Skr. Uppsala Univ. C Organ. Hist. 64, 92–109 (1997)
5. Ball, J., Currie, J., Olver, P.: Null Lagrangians, weak continuity, and variational problems of arbitrary order. J. Funct. Anal. 41(2), 135–174 (1981)
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