Past Applied Analysis and Mechanics Seminar

7 May 2007
17:00
Sergio Conti
Abstract
&nbsp;<font SIZE="2"> The intermediate state of a type-I superconductor is a classical example of energy-driven pattern-formation, first studied by Landau in 1937. Mathematically this can be modeled by a nonconvex functional with a singular perturbation, which physically represents the surface energy. In this talk I shall discuss how a combination of interpolation inequalities and explicit constructions permits to determine the scaling of the minimal energy with respect to the relevant material parameters, and therefore to predict a phase diagram for the observed microstructure. This talk is mainly based on joint work with Rustum Choksi, Robert V. Kohn, and Felix Otto. &nbsp; </font> &nbsp;
  • Applied Analysis and Mechanics Seminar
30 April 2007
17:00
Kewei Zhang
Abstract
&nbsp; 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. &nbsp;
  • Applied Analysis and Mechanics Seminar

Pages