On Tartar's conjecture

Vladimír Šverák

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

On Tartar's conjecture

Vladimír Šverák

Mathematics

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

43 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

Access

10.1016/S0294-1449(16)30208-6

OpenUrl availability

Full text

Cite this

@article{4fb34b7689de4844bcf5a84680d6b3e2,

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",

month = jul,

day = "1",

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

language = "English (US)",

volume = "10",

pages = "405--412",

journal = "Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire",

issn = "0294-1449",

publisher = "Elsevier Masson SAS",

number = "4",

}

TY - JOUR

T1 - On Tartar's conjecture

AU - Šverák, Vladimír

PY - 1993/7/1

Y1 - 1993/7/1

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

UR - http://www.scopus.com/inward/record.url?scp=85011602234&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85011602234&partnerID=8YFLogxK

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

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

M3 - Article

AN - SCOPUS:85011602234

SN - 0294-1449

VL - 10

SP - 405

EP - 412

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

Abstract

Keywords

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this