- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:47
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
28
2012
3
An elliptic variational problem involving level surface area on Riemannian manifolds
Eduardo
Teixeira
Universidade Federal do Ceará, FORTALEZA - CEARA, BRAZIL
Lei
Zhang
University of Florida, GAINESVILLE, UNITED STATES
Monotonicity formula, variational form, free boundary problems
We study a variational problem involving a Dirichlet integral and the area of a level surface on arbitrary $n$-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 $n-8$.
Partial differential equations
General
759
772
10.4171/RMI/690
http://www.ems-ph.org/doi/10.4171/RMI/690