Geodesic
Universal boundary value problem for equations of mathematical physics
Informatics and Automation, Selected topics of mathematical physics and analysis, Tome 285 (2014), pp. 64-88

Voir la notice de l'article provenant de la source Math-Net.Ru

A new statement of a boundary value problem for partial differential equations is discussed. An arbitrary solution to a linear elliptic, hyperbolic, or parabolic second-order differential equation is considered in a given domain of Euclidean space without any constraints imposed on the boundary values of the solution or its derivatives. The following question is studied: What conditions should hold for the boundary values of a function and its normal derivative if this function is a solution to the linear differential equation under consideration? A linear integral equation is defined for the boundary values of a solution and its normal derivative; this equation is called a universal boundary value equation. A universal boundary value problem is a linear differential equation together with a universal boundary value equation. In this paper, the universal boundary value problem is studied for equations of mathematical physics such as the Laplace equation, wave equation, and heat equation. Applications of the analysis of the universal boundary value problem to problems of cosmology and quantum mechanics are pointed out. 
@article{TRSPY_2014_285_a5,
     author = {I. V. Volovich and V. Zh. Sakbaev},
     title = {Universal boundary value problem for equations of mathematical physics},
     journal = {Informatics and Automation},
     pages = {64--88},
     publisher = {mathdoc},
     volume = {285},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2014_285_a5/}
}
TY  - JOUR
AU  - I. V. Volovich
AU  - V. Zh. Sakbaev
TI  - Universal boundary value problem for equations of mathematical physics
JO  - Informatics and Automation
PY  - 2014
SP  - 64
EP  - 88
VL  - 285
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2014_285_a5/
LA  - ru
ID  - TRSPY_2014_285_a5
ER  - 
%0 Journal Article
%A I. V. Volovich
%A V. Zh. Sakbaev
%T Universal boundary value problem for equations of mathematical physics
%J Informatics and Automation
%D 2014
%P 64-88
%V 285
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2014_285_a5/
%G ru
%F TRSPY_2014_285_a5
I. V. Volovich; V. Zh. Sakbaev. Universal boundary value problem for equations of mathematical physics. Informatics and Automation, Selected topics of mathematical physics and analysis, Tome 285 (2014), pp. 64-88. http://geodesic.mathdoc.fr/item/TRSPY_2014_285_a5/