#### 贡献

2018年度邵逸夫数学科学奖颁予路易・卡法雷 (Luis A Caffarelli)，以表彰他在偏微分方程上的突破性工作，包括创立一套正则理论，适用於如蒙日−安培方程等非线性方程，及如障碍问题等的自由边界问题，这些工作影响了该领域整个世代的研究。路易・卡法雷是美国德克萨斯大学奥斯汀分校数学教授。

#### 得奖人获奖介绍

Differential equations are fundamental to large parts of mathematics, physics, and indeed all the sciences. For example, if a physical system is in a certain state, and obeys certain laws, then a differential equation will tell you the state of the system infinitesimally later, and by putting together all these infinitesimal changes one can follow the evolution of the system in time. Or if a static system is held together by certain forces, a differential equation can often say how one part of the system depends on its immediate neighbours, and putting together this local information can give a global description of the system.

The simplest differential equations, known as ordinary differential equations, concern functions that depend on just one variable. For example, if a stone is thrown vertically in the air, then there is an ordinary differential equation that describes how its height varies as a function of time, given its initial height and velocity. However, the most useful equations, known as partial differential equations, concern functions of several variables (such as, for example, three spatial coordinates and one temporal coordinate) and are significantly more complicated as a result. Partial differential equations can be used to model heat flow, fluid motion, electromagnetic waves, quantum mechanics, the shape of soap bubbles, and innumerable other physical phenomena.