Page 1 Next

Displaying 1 – 20 of 22

Showing per page

The asymptotic behaviour of surfaces with prescribed mean curvature near meeting points of fixed and free boundaries

Frank Müller (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We study the shape of stationary surfaces with prescribed mean curvature in the Euclidean 3-space near boundary points where Plateau boundaries meet free boundaries. In deriving asymptotic expansions at such points, we generalize known results about minimal surfaces due to G. Dziuk. The main difficulties arise from the fact that, contrary to minimal surfaces, surfaces with prescribed mean curvature do not meet the support manifold perpendicularly along their free boundary, in general.

The obstacle problem for functions of least gradient

William P. Ziemer, Kevin Zumbrun (1999)

Mathematica Bohemica

For a given domain Ω n , we consider the variational problem of minimizing the L 1 -norm of the gradient on Ω of a function u with prescribed continuous boundary values and satisfying a continuous lower obstacle condition u ψ inside Ω . Under the assumption of strictly positive mean curvature of the boundary Ω , we show existence of a continuous solution, with Holder exponent half of that of data and obstacle. This generalizes previous results obtained for the unconstrained and double-obstacle problems. The...

Currently displaying 1 – 20 of 22

Page 1 Next