Generalized Solutions to Boundary-Value Problems for Quasilinear Elliptic Equations on Noncompact Riemannian Manifolds

In the present work we develop approximation approach to evaluation of solutions to boundary-value problems for quasilinear equations of the elliptic type on arbitrary noncompact Riemannian manifolds. Our technique essentially bases on an approach from the papers of E. A. Mazepa and S. A. Korol’kov...

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Bibliographic Details
Published in:Russian mathematics 2018, Vol.62 (1), p.50-57
Main Author: Mazepa, E. A.
Format: Article
Language:English
Subjects:
Boundary value problems
Dirichlet problem
Mathematical analysis
Mathematics
Mathematics and Statistics
Riemann manifold
Schrodinger equation
Theorems
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Summary:In the present work we develop approximation approach to evaluation of solutions to boundary-value problems for quasilinear equations of the elliptic type on arbitrary noncompact Riemannian manifolds. Our technique essentially bases on an approach from the papers of E. A. Mazepa and S. A. Korol’kov connected with introduction of equivalency classes of functions and representations. On the other hand, it generalizes the method of building of generalized solution to the Dirichlet problem for linear elliptic Laplace–Beltrami and Schrödinger equations in bounded domains in ℝ n , which is described in details in the works of M. V. Keldysh and E. M. Landis.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X18010073