Propagating terraces in a proof of the Gibbons conjecture and related results

P. Poláčik

doi:10.1007/s11784-016-0343-7

Propagating terraces in a proof of the Gibbons conjecture and related results

P. Poláčik

School of Mathematics

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

4 Scopus citations

Abstract

The Gibbons conjecture stating the one-dimensional symmetry of certain solutions of semilinear elliptic equations has been proved by several authors. We show how attractivity properties of minimal propagating terraces of one-dimensional parabolic problems can be used in a proof of a version of this result and related statements.

Original language	English (US)
Pages (from-to)	113-128
Number of pages	16
Journal	Journal of Fixed Point Theory and Applications
Volume	19
Issue number	1
DOIs	https://doi.org/10.1007/s11784-016-0343-7
State	Published - Mar 1 2017

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing.

Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

Keywords

Elliptic equations
Gibbons conjecture
one-dimensional symmetry
propagating terraces
traveling fronts

Publisher link

10.1007/s11784-016-0343-7

Find It

Find It at U of M Libraries

Cite this

@article{18845326a6eb43668e7cc740ee29282d,

title = "Propagating terraces in a proof of the Gibbons conjecture and related results",

abstract = "The Gibbons conjecture stating the one-dimensional symmetry of certain solutions of semilinear elliptic equations has been proved by several authors. We show how attractivity properties of minimal propagating terraces of one-dimensional parabolic problems can be used in a proof of a version of this result and related statements.",

keywords = "Elliptic equations, Gibbons conjecture, one-dimensional symmetry, propagating terraces, traveling fronts",

author = "P. Pol{\'a}{\v c}ik",

year = "2017",

month = mar,

day = "1",

doi = "10.1007/s11784-016-0343-7",

language = "English (US)",

volume = "19",

pages = "113--128",

journal = "Journal of Fixed Point Theory and Applications",

issn = "1661-7738",

publisher = "Springer Science + Business Media",

number = "1",

}

TY - JOUR

T1 - Propagating terraces in a proof of the Gibbons conjecture and related results

AU - Poláčik, P.

PY - 2017/3/1

Y1 - 2017/3/1

N2 - The Gibbons conjecture stating the one-dimensional symmetry of certain solutions of semilinear elliptic equations has been proved by several authors. We show how attractivity properties of minimal propagating terraces of one-dimensional parabolic problems can be used in a proof of a version of this result and related statements.

AB - The Gibbons conjecture stating the one-dimensional symmetry of certain solutions of semilinear elliptic equations has been proved by several authors. We show how attractivity properties of minimal propagating terraces of one-dimensional parabolic problems can be used in a proof of a version of this result and related statements.

KW - Elliptic equations

KW - Gibbons conjecture

KW - one-dimensional symmetry

KW - propagating terraces

KW - traveling fronts

UR - http://www.scopus.com/inward/record.url?scp=84994275802&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84994275802&partnerID=8YFLogxK

U2 - 10.1007/s11784-016-0343-7

DO - 10.1007/s11784-016-0343-7

M3 - Article

AN - SCOPUS:84994275802

SN - 1661-7738

VL - 19

SP - 113

EP - 128

JO - Journal of Fixed Point Theory and Applications

JF - Journal of Fixed Point Theory and Applications

IS - 1

ER -

Propagating terraces in a proof of the Gibbons conjecture and related results

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this