偏微分方程高级研讨班

We propose to organize a high-level, research oriented and concentrated mini-series of courses and seminars in the theory and applications of nonlinear elliptic and parabolic partial differential equations. Of particular interests and emphasizes are the following important topics .that have stumilated much of the recent developments in the field and with many opportunities for further exiciting researches..(i) De Giorgi Conjecture and related subjects including phase field equations, free interface problems and their vector-valued counter parts .such as Ginzburg-Landau equations, theory of harmonic maps and liquid crystals..(ii) Theory of Monge-Ampere equations and optimal mass transport maps as well as their applications in many classical geometric variational problems..(iii) The classical and complex fluid dynamic equations including the well-known Navier-Stokes, the Oldroyd models of viscoelastic fluids and.magneto-hydrodynamic equations.

对于非线性椭圆与抛物偏微分方程我们计划组织一个高水平的，方向明确与集中的几个小课程与研讨班。我们将对以下重要的主题给予特别兴趣与着重，它们激发了此领域的最新发展并在将来有很多机会进一步做更有意义的研究。它们是：.（1）De Giorgi猜想及相关主题，包括相场方程，自由界面问题及其向量值对应部分，如Ginzburg-Landau方程，调和映射和液晶的理论。.（2）Monge-Ampere方程理论和最优质量运势的理论以及他们在许多经典的几何变分问题的应用。.（三）经典的和复杂的流体动力学方程，包括著名的Navier-Stokes方程，粘弹性流体的Oldroyd模型和磁流体动力学方程。