Strongly elliptic linear operators without coercive quadratic forms I. Constant coefficient operators and forms

Gregory C. Verchota

doi:10.4171/JEMS/485

Strongly elliptic linear operators without coercive quadratic forms I. Constant coefficient operators and forms

Gregory C. Verchota

Department of Mathematics

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

1 Scopus citations

Abstract

A family of linear homogeneous fourth order elliptic differential operators L with real constant coefficients, and bounded nonsmooth convex domains Ω are constructed in ℝ⁶ so that the L have no constant coefficient coercive integro-differential quadratic forms over the Sobolev spaces W^{2, 2}, (Ω).

Original language	English (US)
Pages (from-to)	2165-2210
Number of pages	46
Journal	Journal of the European Mathematical Society
Volume	16
Issue number	10
DOIs	https://doi.org/10.4171/JEMS/485
State	Published - 2014

Keywords

Indefinite form
Korn inequality
Lax-Milgram
Legendre-Hadamard
Neumann problem
Null form
Rellich identity
Sum of squares

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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abstract = "A family of linear homogeneous fourth order elliptic differential operators L with real constant coefficients, and bounded nonsmooth convex domains Ω are constructed in ℝ6 so that the L have no constant coefficient coercive integro-differential quadratic forms over the Sobolev spaces W2, 2, (Ω).",

keywords = "Indefinite form, Korn inequality, Lax-Milgram, Legendre-Hadamard, Neumann problem, Null form, Rellich identity, Sum of squares",

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AU - Verchota, Gregory C.

N1 - Publisher Copyright: © European Mathematical Society 2014.

PY - 2014

Y1 - 2014

N2 - A family of linear homogeneous fourth order elliptic differential operators L with real constant coefficients, and bounded nonsmooth convex domains Ω are constructed in ℝ6 so that the L have no constant coefficient coercive integro-differential quadratic forms over the Sobolev spaces W2, 2, (Ω).

AB - A family of linear homogeneous fourth order elliptic differential operators L with real constant coefficients, and bounded nonsmooth convex domains Ω are constructed in ℝ6 so that the L have no constant coefficient coercive integro-differential quadratic forms over the Sobolev spaces W2, 2, (Ω).

KW - Indefinite form

KW - Korn inequality

KW - Lax-Milgram

KW - Legendre-Hadamard

KW - Neumann problem

KW - Null form

KW - Rellich identity

KW - Sum of squares

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M3 - Article

AN - SCOPUS:84908402196

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VL - 16

SP - 2165

EP - 2210

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 10

ER -

Strongly elliptic linear operators without coercive quadratic forms I. Constant coefficient operators and forms

Abstract

Keywords

ASJC Scopus subject areas

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