Victor Isakov
Encyclopedia
Victor Isakov is a mathematician
working in the field of inverse problem
s for partial differential equation
s and related topics (potential theory
, uniqueness of continuation and Carleman estimates, nonlinear functional analysis and calculus of variation). He is currently distinguished professor
in the Department of Mathematics and Statistics at Wichita State University
.
His areas of professional interest include:
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
working in the field of inverse problem
Inverse problem
An inverse problem is a general framework that is used to convert observed measurements into information about a physical object or system that we are interested in...
s for partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s and related topics (potential theory
Potential theory
In mathematics and mathematical physics, potential theory may be defined as the study of harmonic functions.- Definition and comments :The term "potential theory" was coined in 19th-century physics, when it was realized that the fundamental forces of nature could be modeled using potentials which...
, uniqueness of continuation and Carleman estimates, nonlinear functional analysis and calculus of variation). He is currently distinguished professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
in the Department of Mathematics and Statistics at Wichita State University
Wichita State University
Wichita State University is a NCAA Division I public university in Wichita, Kansas with selective admissions. WSU is one of six state universities governed by the Kansas Board of Regents. The current president is Dr. Donald Beggs....
.
His areas of professional interest include:
- Inverse problems of gravimetry (general uniqueness conditions and local solvability theorems) and related problems of imaging including prospecting active part of the brain and the source of noise of the aircraft from exterior measurements of electromagnetic and acoustical fields.
- Inverse problems of conductivityElectrical impedance tomographyElectrical impedance tomography is a medical imaging technique in which an image of the conductivity or permittivity of part of the body is inferred from surface electrical measurements. Typically, conducting electrodes are attached to the skin of the subject and small alternating currents are...
(uniqueness of discontinuous conductivity and numerical methods) and their applications to medical imaging and nondestructive testing of materials for cracks and inclusions. - Inverse scattering problems (uniqueness and stability of penetrable and soft scatterers).
- Finding constitutional laws from experimental data (reconstructing nonlinear partial differential equation from all or some boundary data).
- Uniqueness of the continuation for hyperbolic equations and systems of mathematical physics.
- The inverse option pricing problem.
Publications
Isakov has over 90 publications in print or in preparation as of late 2005, which include:- Increased stability in the continuation of solutions to the Helmholtz equation (with Tomasz Hrycak), Inverse Problems, 20(2004), 697-712.
- Inverse Problems for Partial Differential Equations, Applied Mathematical Sciences (Springer-Verlag), Vol 127, 2nd ed., 2006. ISBN 0-387-25364-5