On some asymptotic representations of solutions to elliptic equations and their applications

Abstract

The question on asymptotic representations of Green's function for classical boundary value problems for second-order elliptic equations depending on a complex parameter is considered. The equations are defined either in a domain with a compact boundary or in the whole space or the half-space. The main asymptotic term is written out. The results can be applied for the study of some inverse problems of recovering point sources in heat and mass transfer problems.

Keywords:

• Helmholtz equation
• boundary value problems
• Green's function
• asymptotics
• inverse problem

AMS SUBJECT CLASSIFICATIONS:

• 35J08
• 35J05
• 35R30

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author is supported by Mathematical Center in Akademgorodok with the Ministry of Science and Higher Education of the Russian Federation [grant number 075-15-2019-1613]. The second author is supported by the Russian Foundation for basic research [grant number 18-01-00620].