title: Higher order Dirichlet type problems for the two-dimensional Helmholtz operator in complex quaternionic analysis
metadata.name: dc.contributor.author
metadata.value: Schneider, Baruch
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-12-06T13:02:22Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-12-06T13:02:22Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Schneider B. Higher order Dirichlet type problems for the two-dimensional Helmholtz operator in complex quaternionic analysis. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 4, pp. 646–658.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.410
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/16747
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: It is well known that the development of methods for solving Dirichlet problems is important
  and relevant for various areas of mathematical physics related to the Laplace equation,
  the Helmholtz equation, the Stokes equation, the Maxwell equation, the Dirac equation,
  and others. In the previous work, the author studied the solvability of Dirichlet problem of
  the first order and the second order in the quaternion analysis. In the present paper studies
  the Dirichlet boundary value problem of high order, associated with the two-dimensional
  Helmholtz equation with complex potential. In this paper, the existence and uniqueness
  and a representation formula for the solution of Dirichlet boundary value problems in the
  two-dimensional case are proved. Most of Dirichlet boundary value problems are focused to
  the 3D case. Note that the case is not a simple consequence of the three-dimensional case.
  For solving the problem, we use the method of orthogonal decomposition of the quaternion
  Sobolev space. This orthogonal decomposition of space is also the basis for the study of
  many elliptic boundary value problems that are in various areas of mathematics and mathematical
  physics. Orthogonal decompositions of the quaternionic-valued Sobolev space with
  respect to the Dirac operator of high order as well as the corresponding orthoprojections
  onto the subspaces of theses decompositions are obtained.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The article was prepared with the financial support of the Technical University of Ostrava, Czech Republic, project "Numbers, geometry and physics".
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 6 (64); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: quaternion analysis
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Helmholtz operator
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: boundary problems of Dirichlet type
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Higher order Dirichlet type problems for the two-dimensional Helmholtz operator in complex quaternionic analysis
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 646-658.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/16747/1/646-658.pdf
resources.format: Adobe PDF
resources.size: 333,06 kB