Harmonic Analysis and Partial Differential Equations

调和分析与偏微分方程。Kenig该提案将是PI对自由边界问题解的正则性研究的延续，最小光滑条件下边值问题的分析，粘性守恒律的Liouville型定理的发展，从傅立叶分析技术的发展来研究非线性色散方程解的定性和定量性质，并使用定量的唯一延拓研究电阻抗断层成像中的安德森局部化和逆问题的方法。 这些偏微分方程出现在量子力学模型，流体力学和层析成像理论等领域，因此这些方程的分析可能有许多应用。

Harmonic Analysis and Partial Differential EquationsProject AbstractCarlos E. KenigThe proposal will be a continuation of the PI's research on the regularity of solutions to free boundary problems, the analysis of boundary value problems under minimal smoothness conditions, the development of Liouville type theorems for viscous conservation laws, the development of techniques from Fourier analysis to study qualitative and quantitative properties of solutions of nonlinear dispersive equations and the use of quantitative unique continuation methods to study Anderson localization and the inverse problem in electrical impedance tomography. These partial differential equations arise in quantum mechanical models, fluid mechanics and tomography theory amongst other areas so the analysis of these equations may have many applications.