Quantitative Runge Approximation and Inverse Problems-Reference-Cited by-同舟云学术

Quantitative Runge Approximation and Inverse Problems

Published:2018-01-19 Issue:20 Volume:2019 Page:6216-6234
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Rüland Angkana¹,Salo Mikko²

Affiliation:

1. Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG

2. Department of Mathematics and Statistics, University of Jyväskylä

Abstract

AbstractIn this short note, we provide a quantitative version of the classical Runge approximation property for second-order elliptic operators. This relies on quantitative unique continuation results and duality arguments. We show that these estimates are essentially optimal. As a model application, we provide a new proof of the result from [8], [2] on stability for the Calderón problem with local data.

Funder

Academy of Finland

H2020 European Research Council

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2019/20/6216/30121098/rnx301.pdf

Reference22 articles.

1. “Stable determination of conductivity by boundary measurements.”;Alessandrini;Appl. Anal.,1988

2. “Single-logarithmic stability for the Calderón problem with local data.”;Alessandrini;J. Inverse Ill-Posed Probl.,2012