On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations

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On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations. / Bobkov, Vladimir; Kolonitskii, Sergey.

In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Vol. 149, No. 5, 2019, p. 1163-1173.

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Author

Bobkov, Vladimir ; Kolonitskii, Sergey. / On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations. In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 2019 ; Vol. 149, No. 5. pp. 1163-1173.

BibTeX

@article{b383e99c9ddf43a4829ae1603ece8c0c,

title = "On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations",

abstract = "In this note, we prove the Payne-type conjecture about the behaviour of the nodal set of least energy sign-changing solutions for the equation in bounded Steiner symmetric domains under the zero Dirichlet boundary conditions. The nonlinearity f is assumed to be either superlinear or resonant. In the latter case, least energy sign-changing solutions are second eigenfunctions of the zero Dirichlet p-Laplacian in ω. We show that the nodal set of any least energy sign-changing solution intersects the boundary of ω. The proof is based on a moving polarization argument.",

keywords = "least energy nodal solution, nodal set, p-Laplacian, Payne conjecture, polarization, second eigenvalue, superlinear",

author = "Vladimir Bobkov and Sergey Kolonitskii",

year = "2019",

doi = "10.1017/prm.2018.88",

language = "English",

volume = "149",

pages = "1163--1173",

journal = "Royal Society of Edinburgh - Proceedings A",

issn = "0308-2105",

publisher = "Cambridge University Press",

number = "5",

}

RIS

TY - JOUR

T1 - On a property of the nodal set of least energy sign-changing solutions for quasilinear elliptic equations

AU - Bobkov, Vladimir

AU - Kolonitskii, Sergey

PY - 2019

Y1 - 2019

N2 - In this note, we prove the Payne-type conjecture about the behaviour of the nodal set of least energy sign-changing solutions for the equation in bounded Steiner symmetric domains under the zero Dirichlet boundary conditions. The nonlinearity f is assumed to be either superlinear or resonant. In the latter case, least energy sign-changing solutions are second eigenfunctions of the zero Dirichlet p-Laplacian in ω. We show that the nodal set of any least energy sign-changing solution intersects the boundary of ω. The proof is based on a moving polarization argument.

AB - In this note, we prove the Payne-type conjecture about the behaviour of the nodal set of least energy sign-changing solutions for the equation in bounded Steiner symmetric domains under the zero Dirichlet boundary conditions. The nonlinearity f is assumed to be either superlinear or resonant. In the latter case, least energy sign-changing solutions are second eigenfunctions of the zero Dirichlet p-Laplacian in ω. We show that the nodal set of any least energy sign-changing solution intersects the boundary of ω. The proof is based on a moving polarization argument.

KW - least energy nodal solution

KW - nodal set

KW - p-Laplacian

KW - Payne conjecture

KW - polarization

KW - second eigenvalue

KW - superlinear

UR - http://www.scopus.com/inward/record.url?scp=85060012777&partnerID=8YFLogxK

U2 - 10.1017/prm.2018.88

DO - 10.1017/prm.2018.88

M3 - Article

AN - SCOPUS:85060012777

VL - 149

SP - 1163

EP - 1173

JO - Royal Society of Edinburgh - Proceedings A

JF - Royal Society of Edinburgh - Proceedings A

SN - 0308-2105

IS - 5

ER -

ID: 38486825