Mathematical Sciences: Bergman Space Inequalities

Wilson将证明加权范数不等式，它显示了某些类别的偏微分方程的解的内部平滑是如何由其边界数据的大小控制的。这使得人们可以测量pde精确解的数值近似的收敛速度，并确定边界数据的扰动如何影响收敛速度。偏微分方程是物理世界数学建模的基础。数学分析的作用与其说是创建方程，不如说是提供关于解的定性和定量信息。这可能包括回答关于独特性、平滑性和增长性的问题。此外，分析常常发展出解的近似方法和对这些近似精度的估计。

Wilson DMS-9501107 Wilson will prove weighted norm inequalities that show how the interior smoothness of solutions of certain classes of partial differential equations are controlled by the size of their boundary data. This allows one to gauge the speed of convergence of numerical approximations to the exact solutions of the pde, and to determine how perturbations of boundary data effects the rate of convergence. Partial differential equations form a basis for mathematical modeling of the physical world. The role of mathematical analysis is not so much to create the equations as it is to provide qualitative and quantitative information about the solutions. This may include answers to questions about uniqueness, smoothness and growth. In addition, analysis often develops methods for approximation of solutions and estimates on the accuracy of these approximations.