Pseudo-differential equations and conical potentials: 2-dimensional case

We consider two-dimensional elliptic pseudo-differential equation in a plane sector. Using a special representation for an elliptic symbol and the formula for a general solution we study the Dirichlet problem for such equation. This problem was reduced to a system of linear integral equations and th...

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Main Author:	Vladimir B. Vasilyev
Format:	Article
Language:	English
Published:	AGH Univeristy of Science and Technology Press 2019-01-01
Series:	Opuscula Mathematica
Subjects:	pseudo-differential equation wave factorization dirichlet problem system of linear integral equations
Online Access:	https://www.opuscula.agh.edu.pl/vol39/1/art/opuscula_math_3908.pdf

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record_format	Article
spelling	doaj-1288bab8470d4d65a39017c49a92e3632020-11-25T02:19:07ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742019-01-01391109124https://doi.org/10.7494/OpMath.2019.39.1.1093908Pseudo-differential equations and conical potentials: 2-dimensional caseVladimir B. Vasilyev0https://orcid.org/0000-0001-9351-8084Chair of Differential Equations, Belgorod National Research State University, Studencheskaya 14/1, Belgorod 308007, RussiaWe consider two-dimensional elliptic pseudo-differential equation in a plane sector. Using a special representation for an elliptic symbol and the formula for a general solution we study the Dirichlet problem for such equation. This problem was reduced to a system of linear integral equations and then after some transformations to a system of linear algebraic equations. The unique solvability for the Dirichlet problem was proved in Sobolev-Slobodetskii spaces and a priori estimate for the solution is given.https://www.opuscula.agh.edu.pl/vol39/1/art/opuscula_math_3908.pdfpseudo-differential equationwave factorizationdirichlet problemsystem of linear integral equations
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Vladimir B. Vasilyev
spellingShingle	Vladimir B. Vasilyev Pseudo-differential equations and conical potentials: 2-dimensional case Opuscula Mathematica pseudo-differential equation wave factorization dirichlet problem system of linear integral equations
author_facet	Vladimir B. Vasilyev
author_sort	Vladimir B. Vasilyev
title	Pseudo-differential equations and conical potentials: 2-dimensional case
title_short	Pseudo-differential equations and conical potentials: 2-dimensional case
title_full	Pseudo-differential equations and conical potentials: 2-dimensional case
title_fullStr	Pseudo-differential equations and conical potentials: 2-dimensional case
title_full_unstemmed	Pseudo-differential equations and conical potentials: 2-dimensional case
title_sort	pseudo-differential equations and conical potentials: 2-dimensional case
publisher	AGH Univeristy of Science and Technology Press
series	Opuscula Mathematica
issn	1232-9274
publishDate	2019-01-01
description	We consider two-dimensional elliptic pseudo-differential equation in a plane sector. Using a special representation for an elliptic symbol and the formula for a general solution we study the Dirichlet problem for such equation. This problem was reduced to a system of linear integral equations and then after some transformations to a system of linear algebraic equations. The unique solvability for the Dirichlet problem was proved in Sobolev-Slobodetskii spaces and a priori estimate for the solution is given.
topic	pseudo-differential equation wave factorization dirichlet problem system of linear integral equations
url	https://www.opuscula.agh.edu.pl/vol39/1/art/opuscula_math_3908.pdf
work_keys_str_mv	AT vladimirbvasilyev pseudodifferentialequationsandconicalpotentials2dimensionalcase
_version_	1724878434252881920

Pseudo-differential equations and conical potentials: 2-dimensional case

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