Monotonicity and enclosure methods for the p-Laplace equation

Tommi Olavi Brander; Bastian Harrach; Manas Kar; Mikko Salo

doi:10.1137/17M1128599

Monotonicity and enclosure methods for the p-Laplace equation

Tommi Olavi Brander, Bastian Harrach, Manas Kar, Mikko Salo

Research output: Contribution to journal › Journal article › Research › peer-review

151 Downloads (Pure)

Abstract

We show that the convex hull of a monotone perturbation of a homogeneous background conductivity in the p-conductivity equation is determined by knowledge of the nonlinear Dirichlet-Neumann operator. We give two independent proofs: one is based on the monotonicity method and the other on the enclosure method. Our results are constructive and require no jump or smoothness properties on the conductivity perturbation or its support.

Original language	English
Journal	S I A M Journal on Applied Mathematics
Volume	78
Issue number	2
Pages (from-to)	742-758
ISSN	0036-1399
DOIs	https://doi.org/10.1137/17M1128599
Publication status	Published - 2018

Keywords

p-Laplace equation
Inclusion detection
Monotonicity method
Enclosure method

Access to Document

10.1137/17M1128599

17m1128599Final published version, 358 KB

OpenUrl availability

Full text

Cite this

@article{c0c9508f7a3843a2b9e37f1c3ea0beb4,

title = "Monotonicity and enclosure methods for the p-Laplace equation",

abstract = "We show that the convex hull of a monotone perturbation of a homogeneous background conductivity in the p-conductivity equation is determined by knowledge of the nonlinear Dirichlet-Neumann operator. We give two independent proofs: one is based on the monotonicity method and the other on the enclosure method. Our results are constructive and require no jump or smoothness properties on the conductivity perturbation or its support.",

keywords = "p-Laplace equation, Inclusion detection, Monotonicity method, Enclosure method",

author = "Brander, {Tommi Olavi} and Bastian Harrach and Manas Kar and Mikko Salo",

year = "2018",

doi = "10.1137/17M1128599",

language = "English",

volume = "78",

pages = "742--758",

journal = "S I A M Journal on Applied Mathematics",

issn = "0036-1399",

publisher = "Society for Industrial and Applied Mathematics",

number = "2",

}

TY - JOUR

T1 - Monotonicity and enclosure methods for the p-Laplace equation

AU - Brander, Tommi Olavi

AU - Harrach, Bastian

AU - Kar, Manas

AU - Salo, Mikko

PY - 2018

Y1 - 2018

N2 - We show that the convex hull of a monotone perturbation of a homogeneous background conductivity in the p-conductivity equation is determined by knowledge of the nonlinear Dirichlet-Neumann operator. We give two independent proofs: one is based on the monotonicity method and the other on the enclosure method. Our results are constructive and require no jump or smoothness properties on the conductivity perturbation or its support.

AB - We show that the convex hull of a monotone perturbation of a homogeneous background conductivity in the p-conductivity equation is determined by knowledge of the nonlinear Dirichlet-Neumann operator. We give two independent proofs: one is based on the monotonicity method and the other on the enclosure method. Our results are constructive and require no jump or smoothness properties on the conductivity perturbation or its support.

KW - p-Laplace equation

KW - Inclusion detection

KW - Monotonicity method

KW - Enclosure method

U2 - 10.1137/17M1128599

DO - 10.1137/17M1128599

M3 - Journal article

SN - 0036-1399

VL - 78

SP - 742

EP - 758

JO - S I A M Journal on Applied Mathematics

JF - S I A M Journal on Applied Mathematics

IS - 2

ER -

Monotonicity and enclosure methods for the p-Laplace equation

Abstract

Keywords

Access to Document

OpenUrl availability

Fingerprint

Cite this