We study a variational problem involving a Dirichlet integral and the area of a level surface on arbitrary -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 .
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. 759–772DOI 10.4171/RMI/690