JournalsrmiVol. 28, No. 3pp. 759–772

An elliptic variational problem involving level surface area on Riemannian manifolds

  • Eduardo V. Teixeira

    Universidade Federal do Ceará, Fortaleza, Brazil
  • Lei Zhang

    University of Florida, Gainesville, USA
An elliptic variational problem involving level surface area on Riemannian manifolds cover
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Abstract

We study a variational problem involving a Dirichlet integral and the area of a level surface on arbitrary nn-dimensional Riemannian manifolds. We prove optimal regularity results for minimizers and derive a jump condition along the level surface. We also obtain smoothness of the interface up to a small singular set of Hausdorff dimension less then or equal to n8n-8.

Cite this article

Eduardo V. Teixeira, Lei Zhang, An elliptic variational problem involving level surface area on Riemannian manifolds. Rev. Mat. Iberoam. 28 (2012), no. 3, pp. 759–772

DOI 10.4171/RMI/690