Singular Poisson equations on Finsler–Hadamard manifolds

In the first part of the paper we study the reflexivity of Sobolev spaces on non-compact and not necessarily reversible Finsler manifolds. Then, by using direct methods in the calculus of variations, we establish uniqueness, location and rigidity results for singular Poisson equations involving the...

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Bibliographic Details
Published in:	Calculus of variations and partial differential equations Vol. 54; no. 2; pp. 1219 - 1241
Main Authors:	Farkas, Csaba, Kristály, Alexandru, Varga, Csaba
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01-10-2015
Subjects:	Analysis Calculus of Variations and Optimal Control; Optimization Control Mathematical and Computational Physics Mathematics Mathematics and Statistics Systems Theory Theoretical 58J60 53C60 58J05
Online Access:	Get full text
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Summary:	In the first part of the paper we study the reflexivity of Sobolev spaces on non-compact and not necessarily reversible Finsler manifolds. Then, by using direct methods in the calculus of variations, we establish uniqueness, location and rigidity results for singular Poisson equations involving the Finsler–Laplace operator on Finsler–Hadamard manifolds having finite reversibility constant.
ISSN:	0944-2669 1432-0835
DOI:	10.1007/s00526-015-0823-4