On some semi-explicit quasiconvex functions with prescribed zero sets
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Mon, 30/04/2007 17:00 |
Kewei Zhang (Sussex) |
Applied Analysis and Mechanics Seminar  |
L1 |
| 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. | |||