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Remark on the anisotropic prescribed mean curvature equation on arbitrary domains

Marquardt, T. (2009). Remark on the anisotropic prescribed mean curvature equation on arbitrary domains. Mathematische Zeitschrift, online first. doi:10.1007/s00209-009-0476-0.

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Creators:
Marquardt, Thomas1, Author
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012

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Abstract: In this article we consider the Dirichlet problem for hypersurfaces of aniso- tropic prescribed mean curvature H = H(x, u, N) depending on $${x \in \varOmega \subset \mathbb {R}^n}$$, the height u of the hypersurface M = graph u over $${\varOmega}$$ and the unit normal N to M at (x, u). We give a condition relating H and the mean curvature of $${\partial \varOmega}$$ that guarantees the existence of smooth solutions even for not necessarily convex domains.

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Dates: 2009-01-22
Publication Status: Published in print
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Identifiers: eDoc: 426874
DOI: 10.1007/s00209-009-0476-0
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Title: Mathematische Zeitschrift
Source Genre: Journal
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Pages: - Volume / Issue: online first Sequence Number: - Start / End Page: - Identifier: ISSN: 1432-1823