Global solutions to the heat flow for $m$-harmonic maps and regularity
Verena BoegeleinFrank DuzaarChristoph Scheven
58E2058J3535K5135B40$m$-harmonic mapsgradient flowglobal solutionsasymptotic behavior
In this paper, we establish the existence of global weak solutions to the heat flow for $m$-harmonic maps from a compact $m$-dimensional Riemannian manifold $\Omega$ with non-empty boundary $\partial\Omega$ into a compact Riemannian manifold $N$ without boundary subject to a Cauchy-Dirichlet condition posed on $\partial_{par}\Omega_{\infty}$. Moreover, in the case that $N$ has non-positive sectional curvature, we construct a solution with H\"older continuous spatial gradient.
Indiana University Mathematics Journal
2012
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10.1512/iumj.2012.61.4819
10.1512/iumj.2012.61.4819
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Indiana Univ. Math. J. 61 (2012) 2157 - 2210
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