p-Harmonic obstacle problems
Tóm tắt
Let Ω denote a bounded domain in some Riemannian manifold X with smooth boundary δω and consider a submanifold Y of Euclidean space RL with or without boundary. We show that if U: Ω → Y minimizes the penergy functional
$$E_p (U,\Omega ): = \int\limits_\Omega {\left\| {DU} \right\|^p dVol}$$
for smooth boundary data g: δω → Y, then U is continuous in a neighborhood of δω. This completes the interior partial regularity results of Part I. As an application we obtain an existence theorem concerning small solutions of the Dirichlet problem for pharmonic maps.
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