调和分析与偏微分方程

The main purpose of this program is to study the recent developments.and connections between two related areas from harmonic analysis and.partial differential equations. As is well known, there have been a great many applications of singular integrals, Hardy spaces and BMO in.the study of boundary value problems, with minimal smoothness assumptions on the coefficients, or on the boundary of the domain in question. These problems are of interest both because of their.theoretical importance, and in view of their applied applications, and they have turned out to have profound and fascinating connections with many branches of analysis, especially harmonic analysis. Techniques from harmonic analysis have proved to be extremely useful in their studies.Some new results are obtained in the following aspects: Heat flows in harmonic maps, Hp boundary value Neumann problems for Schr鰀inger.equations with singular potential on Lipschitz domains, Regularity of.solutions to the second order elliptic equations with discontinuous.coefficients with function in Hardy space on right side, Decay estimates.of Fourier transforms of measures with non-smooth densities on hypersurface, Some properties of singular integral operators related to BMO functions, Unique continuation of Schr鰀inger equations, Atomic decomposition of certain kind of Besov spaces.

（1）用调和分析的近代进展，进一步研究振荡积分及其对色散方程的应用，后者包括薛丁穹匠獭dV 方程、波尔格方程等，研究它们在各种巴拿哈空间上的整体适定性与局部适定性。（2）研究区域上的哈代空间以及它们在偏微分方程理论上的应用，包括在非光滑区域系依锟死潮咧滴侍庥肱狄谅咧滴侍獾墓兰啤