Mon, 30 Apr 2007
17:00
17:00
L1
On some semi-explicit quasiconvex functions with prescribed zero sets
Kewei Zhang
(Sussex)
Abstract
For a given Lipschitz graph over a subspace without rank-one matrices with
reasonably small Lipschitz constant, we construct quasiconvex functions of
quadratic growth whose zero sets are exactly the Lipschitz graph by using a
translation method. The gradient of the quasiconvex function is strictly
quasi-monotone. When the graph is a smooth compact manifold, the quasiconvex
function equals the squared distance function near the graph.
The corresponding variational integrals satisfy the Palais-Smale compactness
condition under the homogeneous natural boundary condition.