Abstract
AbstractIt is known that in order for a solution of a boundary value problems for elliptic equations in unbounded domains to be unique, it is necessary to impose additional constraints on the behavior, of solutions at infinity. Such constrains may be qualitatively different.In [1] it was noticed that the assumption that the solutions should be positive for sufficiently large arguments may also serve as a condition that guarantees the uniqueness of solutions. The present report explains an investigation of the conditions on boundary value problems whose fulfillment guarantees the validity of such uniqueness theorems for the biharmonic equation. For harmonic functions that satisfy the Dirichlet or Neumann boundary conditions, there are no such uniqueness theorems. But they can exist for simplest nonlocal boundary value problems for harmonic functions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
