Positivity and strong ellipticity

A. F.M. Ter Elst; Derek W. Robinson; Yueping Zhu

doi:10.1090/S0002-9939-05-08180-3

Positivity and strong ellipticity

A. F.M. Ter Elst^*, Derek W. Robinson, Yueping Zhu

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

We consider partial differential operators H = - div(C▽) in divergence form on R^d with a positive-semidefinite, symmetric, matrix C of real Z_∞-coefficients, and establish that H is strongly elliptic if and only if the associated semigroup kernel satisfies local lower bounds, or, if and only if the kernel satisfies Gaussian upper and lower bounds.

Original language	English
Pages (from-to)	707-714
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	134
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-05-08180-3
Publication status	Published - Mar 2006

Access to Document

10.1090/S0002-9939-05-08180-3

Cite this

@article{0f18b4f1a8644fa482cdfac7eaf37825,

title = "Positivity and strong ellipticity",

abstract = "We consider partial differential operators H = - div(C▽) in divergence form on Rd with a positive-semidefinite, symmetric, matrix C of real Z∞-coefficients, and establish that H is strongly elliptic if and only if the associated semigroup kernel satisfies local lower bounds, or, if and only if the kernel satisfies Gaussian upper and lower bounds.",

keywords = "Elliptic operator, Kernel, Lower bounds, Semigroup, Upper bounds",

author = "\{Ter Elst\}, \{A. F.M.\} and Robinson, \{Derek W.\} and Yueping Zhu",

year = "2006",

month = mar,

doi = "10.1090/S0002-9939-05-08180-3",

language = "English",

volume = "134",

pages = "707--714",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "3",

}

TY - JOUR

T1 - Positivity and strong ellipticity

AU - Ter Elst, A. F.M.

AU - Robinson, Derek W.

AU - Zhu, Yueping

PY - 2006/3

Y1 - 2006/3

N2 - We consider partial differential operators H = - div(C▽) in divergence form on Rd with a positive-semidefinite, symmetric, matrix C of real Z∞-coefficients, and establish that H is strongly elliptic if and only if the associated semigroup kernel satisfies local lower bounds, or, if and only if the kernel satisfies Gaussian upper and lower bounds.

AB - We consider partial differential operators H = - div(C▽) in divergence form on Rd with a positive-semidefinite, symmetric, matrix C of real Z∞-coefficients, and establish that H is strongly elliptic if and only if the associated semigroup kernel satisfies local lower bounds, or, if and only if the kernel satisfies Gaussian upper and lower bounds.

KW - Elliptic operator

KW - Kernel

KW - Lower bounds

KW - Semigroup

KW - Upper bounds

UR - http://www.scopus.com/inward/record.url?scp=33644780616&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-05-08180-3

DO - 10.1090/S0002-9939-05-08180-3

M3 - Article

SN - 0002-9939

VL - 134

SP - 707

EP - 714

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 3

ER -

Positivity and strong ellipticity

Abstract

Access to Document

Other files and links

Fingerprint

Cite this