Open AccessKarp's Theorem in Inverse Obstacle Scattering Problems
Author(s) -
Jeeyoung Shin
Publication year - 2019
Publication title -
journal of advances in mathematics
Language(s) - English
Resource type - Journals
ISSN - 2347-1921
DOI - 10.24297/jam.v17i0.8399
Subject(s) - mathematics , monotonic function , eigenvalues and eigenvectors , obstacle , inverse , inverse scattering problem , continuation , operator (biology) , laplace transform , scattering theory , inverse laplace transform , pure mathematics , inverse problem , mathematical analysis , scattering , computer science , biochemistry , chemistry , physics , geometry , quantum mechanics , repressor , political science , transcription factor , law , gene , programming language , optics
In this work, we provide a proof of the so-called Karp's theorem in a different approach. We use the unique continuation principle together with the monotonicity of eigenvalues for the negative Laplace operator. This method is new and would be applicable to other types of inverse scattering problems.