Journal ArticleDOI
Long-time existence for a solution of the equation of evolution of harmonic maps into an ellipsoid
Reads0
Chats0
TLDR
In this article, the authors prove the existence of a smooth solution of the equation of evolution of harmonic maps if the initial data lies in a compact subset of the upper hemisphere of an ellispoid.Abstract:
This paper is concerned with the evolution of harmonic maps from an open set Ω of ℝm into an n-dimensionnal ellipsoid
$$N = \left\{ {u = (u_I ,u_{II} ) \in \mathbb{R}^n \times \mathbb{R}/u_I^2 + \frac{{u_{II}^2 }}{{a^2 }} = 1} \right\}$$
where a ∈ (0, 1] We prove the existence of a smooth solution of the equation of evolution of harmonic maps if the initial data lies in a compact subset of the upper hemisphere of an ellispoid.read more
References
More filters
Book
Harmonic Maps of Manifolds with Boundary
TL;DR: In this article, the heat equation for manifolds and growth estimates and convergence of growth estimates are discussed.Harmonic maps, function spaces, Semi-elliptic and parabolic equations, and heat equation are presented.
Journal ArticleDOI
Finite-time blow-up of the heat flow of harmonic maps from surfaces
Journal ArticleDOI
Harmonic mappings and minimal submanifolds
Journal ArticleDOI
Uniqueness and Stability of Harmonic Maps and Their Jacobi Fields.
Willi Jäger,Helmut Kaul +1 more
TL;DR: In this paper, an estimate of the distances of Riemannian manifolds by the distance of their boundary values was proved using a maximum principle. But it was not shown that the maximum principle can be used to estimate the distance between the norm of Jacobi fields along harmonic maps.