2018
DOI: 10.1016/j.aml.2017.09.012
|View full text |Cite
|
Sign up to set email alerts
|

Inverse problem of potential theory

Abstract: P. Novikov in 1938 has proved that if u 1 (x) = u 2 (x) for |x| > R, where R > 0 is a large number,are bounded, connected, smooth domains, starshaped with respect to a common point, then D 1 = D 2 . Here B R := {x : |x| ≤ R}. Our basic results are: a) the removal of the assumption about star-shapeness of D j , b) a new approach to the problem, c) the construction of counter-examples for a similar problem in which g 0 is replaced by g = e ik|x−y| 4π|x−y| , where k > 0 is a fixed constant. MSC: 35J05, 35R30

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1

Citation Types

0
1
0

Year Published

2019
2019
2019
2019

Publication Types

Select...
2

Relationship

0
2

Authors

Journals

citations
Cited by 2 publications
(1 citation statement)
references
References 9 publications
0
1
0
Order By: Relevance
“…(15) The employed iterative method for minimization problem is not specified in detail as it is common issue in bibliographic references concerning inverse problems (Gao et al 2016, Nowak 2017, Ramm 2018 and it is out of the scope of this research.…”
Section: 23mentioning
confidence: 99%
“…(15) The employed iterative method for minimization problem is not specified in detail as it is common issue in bibliographic references concerning inverse problems (Gao et al 2016, Nowak 2017, Ramm 2018 and it is out of the scope of this research.…”
Section: 23mentioning
confidence: 99%