On the Strong Solvability of a Nonlocal Boundary Value Problem for the Laplace Equation in an Unbounded Domain

Bilalov B. T., Nasibova N. P., Alili V. Q.

Journal of Contemporary Applied Mathematics, vol.15, no.1, pp.92-106, 2025 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.62476/jcam.151.7
  • Journal Name: Journal of Contemporary Applied Mathematics
  • Journal Indexes: Scopus
  • Page Numbers: pp.92-106
  • Keywords: nonlocal problem, space, strong solution Laplace equation, weighted Sobolev
  • Yıldız Technical University Affiliated: No

Abstract

In this work a nonlocal problem for the Laplace equation in an unbounded domain is considered. The notion of a strong solution of this problem is defined. Using the Fourier method, we prove the correct solvability of the considered problem in Sobolev spaces generated by a weighted mixed-norm. This problem in the classical formulation was previously considered by E. I. Moiseev [1]. The same type of problem was considered in the work of M. E. Lerner and O. A. Repin [2].