On some semi-explicit quasiconvex functions with prescribed zero sets

30 April 2007
Kewei Zhang
  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.  
  • Applied Analysis and Mechanics Seminar