Singular Poisson equations on Finsler–Hadamard manifolds

Farkas, Csaba and Kristály, Alexandru and Varga, Csaba (2015) Singular Poisson equations on Finsler–Hadamard manifolds. Calculus of Variations and Partial Differential Equations, 54 (2). pp. 1219-1241. ISSN 0944-2669

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Abstract

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.

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