Heat Flows and Relaxed Energies for Harmonic Maps
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 7)
In this paper we construct weak solutions for the heat flow associated with relaxed energies for harmonic maps between B3 and S2. Nonuniqueness results for such solutions are also given.
KeywordsManifold Radon Nales
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- F. Bethuel, H. Brezis, J.M. Coron, Relaxed energies for harmonic maps, Variational Problems, Paris June 1988, H. Berestycki, J.M. Coron, I. Ekeland Eds, Birkhäuser.Google Scholar
- J.M. Coron, Nonuniqueness for the heat flow of harmonic maps, Annales IHP, Analyse Non Linéaire, to appear.Google Scholar
- W.Y. Ding, Blow-up of solutions of heat flows for harmonic maps, preprint.Google Scholar
- M. Giaquinta, G. Modica, J. Soucek, Cartesian currents and variational problems for mappings into spheres, preprints, 1989.Google Scholar
- M. Giaquinta, G. Modica, J. Soucek, The Dirichlet energy of mappings with values into the sphere, preprint, 1989.Google Scholar
- K. Horihata and N. Kikuchi, A construction of solutions satisfying a Caccioppoli inequality for nonlinear parabolic equations associated to a variational functional of harmonic type, preprint.Google Scholar
- J. Keller, J. Rubinstein, P. Sternberg, Reaction-diffusion processes and evolution to harmonic maps, preprint.Google Scholar
- L. Simon, Lectures on geometric measure theory, Proc. of the Centre for Mathematical Analysis, Australian National University 3 (1983).Google Scholar
- M. Struwe, The evolution of harmonic maps: existence, partial regularity and singularities, this volume.Google Scholar
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