On Tartar's conjecture

Vladimír Šverák

doi:10.1016/S0294-1449(16)30208-6

On Tartar's conjecture

Vladimír Šverák

School of Mathematics

Research output: Contribution to journal › Article › peer-review

45 Scopus citations

Abstract

We prove that the only probability measures supported at connected subsets of 2 × 2 matrices without rank-one connections and commuting with the determinant are Dirac masses. We also prove some regularity results for fully nonlinear 2 × 2 elliptic systems of the first order.

Original language	English (US)
Pages (from-to)	405-412
Number of pages	8
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	10
Issue number	4
DOIs	https://doi.org/10.1016/S0294-1449(16)30208-6
State	Published - Jul 1 1993

Keywords

Young measures
compactness
regularity

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10.1016/S0294-1449(16)30208-6

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title = "On Tartar's conjecture",

abstract = "We prove that the only probability measures supported at connected subsets of 2 × 2 matrices without rank-one connections and commuting with the determinant are Dirac masses. We also prove some regularity results for fully nonlinear 2 × 2 elliptic systems of the first order.",

keywords = "Young measures, compactness, regularity",

author = "Vladim{\'i}r {\v S}ver{\'a}k",

year = "1993",

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doi = "10.1016/S0294-1449(16)30208-6",

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AU - Šverák, Vladimír

PY - 1993/7/1

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N2 - We prove that the only probability measures supported at connected subsets of 2 × 2 matrices without rank-one connections and commuting with the determinant are Dirac masses. We also prove some regularity results for fully nonlinear 2 × 2 elliptic systems of the first order.

AB - We prove that the only probability measures supported at connected subsets of 2 × 2 matrices without rank-one connections and commuting with the determinant are Dirac masses. We also prove some regularity results for fully nonlinear 2 × 2 elliptic systems of the first order.

KW - Young measures

KW - compactness

KW - regularity

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U2 - 10.1016/S0294-1449(16)30208-6

DO - 10.1016/S0294-1449(16)30208-6

M3 - Article

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SN - 0294-1449

VL - 10

SP - 405

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JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

IS - 4

ER -

On Tartar's conjecture

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