Monotonicity and enclosure methods for thebfitp -laplace equationast

Tommi Brander; Bastian Harrach; Manas Kar; Mikko Salo

doi:10.1137/17M1128599

Monotonicity and enclosure methods for thebfitp -laplace equation^ast

Tommi Brander, Bastian Harrach, Manas Kar, Mikko Salo

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

37 Scopus citations

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
Pages (from-to)	742-758
Number of pages	17
Journal	SIAM Journal on Applied Mathematics
Volume	78
Issue number	2
DOIs	https://doi.org/10.1137/17M1128599
State	Published - 2018
Externally published	Yes

Keywords

Enclosure method
Inclusion detection
Monotonicity method
P-Laplace equation

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10.1137/17M1128599

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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 = "Enclosure method, Inclusion detection, Monotonicity method, P-Laplace equation",

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AU - Brander, Tommi

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 - Enclosure method

KW - Inclusion detection

KW - Monotonicity method

KW - P-Laplace equation

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DO - 10.1137/17M1128599

M3 - Article

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JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

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Monotonicity and enclosure methods for thebfitp -laplace equation^ast

Abstract

Keywords

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