Abstract
This paper is concerned with the initial — boundary value problem for the parabolic system associated with harmonic mappings of Riemannian manifolds. We prove the existence of solutions u(x,t) for all time and verify that u(·,t) tends to a harmonic mapping u∞(·), as t→∞, which assumes the prescribed boundary values. The assumption on the Riemannian manifolds are the same as in the elliptic case.
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Jost, J. Ein Existenzbeweis für harmonische Abbildungen, die ein Dirichletproblem lösen, mittels der Methode des Wärmeflusses. Manuscripta Math 34, 17–25 (1981). https://doi.org/10.1007/BF01168706
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DOI: https://doi.org/10.1007/BF01168706