Korolkov S.A., Losev A.G. Solutions of elliptic partial differential equations on riemannian manifolds with ends

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Korolkov Sergey Alexeevich 

Candidate of Physics and Mathematics, Associate Professor, Chair of Mathematical Analysis and Function Theory, Volgograd State University
sergei.korolkov@rambler.ru
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Losev Alexander Georgievich

Doctor of Physics and Mathematics, Professor, Chair of Mathematical Analysis and Function Theory, Dean of Mathematics and Information Technologies Department, Volgograd State University 
alexander. This email address is being protected from spambots. You need JavaScript enabled to view it.
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. We study solutions of elliptic PDE (L-harmonic functions) on arbitrary noncompact Riemannian manifolds with finitely many ends. We establish some existence and uniqueness results, and obtain sharp dimension estimates for L-harmonic functions on such manifolds.

Key words: Boundary problems, Liouville type theorem, Riemannian manifolds, L-harmonic functions, L-massive sets.

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Solutions of elliptic partial differential equations on Riemannian manifolds with ends by Korolkov S.A., Losev A.G. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English:  Science Journal of Volgograd State University. Mathematics. Physics. №1  (14) 2011 pp. 23-40

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