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- Title
EXISTENCE OF THE FIRST EIGENVALUE OF THE EIGENVALUE PROBLEM FOR THE LAPLACE-BELTRAMI OPERATOR ON THE UNIT SPHERE.
- Authors
BODZIOCH, MARIUSZ; BORSUK, MIKHAIL; JANKOWSKI, SEBASTIAN
- Abstract
In this paper we formulate and prove that there exists the first positive eigenvalue of the eigenvalue problem with oblique derivative for the Laplace-Beltrami operator on the unit sphere. The first eigenvalue plays a major role in studying the asymptotic behaviour of solutions of oblique derivative problems in cone-like domains. Our work is motivated by the fact that the precise solutions decreasing rate near the boundary conical point is dependent on the first eigenvalue.
- Subjects
EIGENVALUES; HOUGH functions; EIGENFREQUENCIES; HILL determinant; JACOBI method
- Publication
Studia Scientiarum Mathematicarum Hungarica, 2018, Vol 55, Issue 3, p374
- ISSN
0081-6906
- Publication type
Article
- DOI
10.1556/012.2018.55.3.1390