Mathematical Sciences: Application of the Mulilayer Free Boundary Method to Nonlinear Elliptic Equations in Convex Domains

本课题研究的是 一类非线性椭圆型方程及其变分 涉及解的重排的导数的问题， 以及与凸对称化有关的问题。 主要的重点是放在变分问题， 可由多层自由边界序列逼近 问题 水平面的规则性和结构 将研究解决办法。 本课题的研究动机是建立一个准静态的 热核聚变中约束环形等离子体的平衡 研究和旋转流体流动的研究。 技术 所要解决的问题在以下领域具有根本性影响： 例如聚变能。

This project is concerned with the regularity theory for a class of nonlinear elliptic equations and associated variational problems involving derivatives of the rearrangement of solutions, as well as related questions concerning convex symmetrization. The main emphasis is to be placed on variational problems which are approximable by sequences of multilayer free boundary problems. Regularity and structure of the level surfaces of solutions will be studied. This project has been motivated by a model of quasi static equilibrium of confined toroidal plasmas in thermonuclear fusion research, and the study of rotational fluid flow. The technical questions to be addressed have fundamental implications in areas such as fusion energy.