报告题目: |
A degenerate Dirichlet boundary value problem for an elliptic equation whose principal part is the minimal surface operator |
报告人: |
Denis Serre |
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Professor
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报告时间: |
2010-01-11 15:45 |
报告地点: |
清华大学科学馆104报告厅 |
主办单位: |
清华大学周培源应用数学研究中心 |
简介: |
We consider an elliptic PDE whose principal part is the minimal surface operator, in a planar domain. The Dirichlet boundary value problem describes hypersurfaces in R^4, having a rotational symmetry, such that one of the principal curvature is the mean of the two other ones. It also describes the self-similar flow of a von Karman gas. We show that the homogeneous Dirichlet problem is well-posed in every uniformly convex domain. There are two main difficulties : one the one hand, the lack of uniform ellipticity, and on the other hand the singularity of the boundary condition. Strangely enough, the whole jet of the solution at the boundary is computable explicitly. |
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