p-ellipticity for complex valued elliptic PDEs and systems

对于复值椭圆型偏微分方程和系统的可解性理论，人们的理解程度明显低于实系数等价标量椭圆型理论。这是由于在标量实际情况下缺乏某些可用的工具，如极大值原理或De Giorgi-Nash-Moser正则性理论。近年来，p-椭圆性的新概念使椭圆复值偏微分方程的建立取得了重大进展。该项目的目的是进一步探索这一突破及其对这些偏微分方程在正则/诺伊曼边界条件下的可解性的影响，以及可解性的外推问题。该项目将关注的第二个主题是椭圆系统的p椭圆性，特别关注特定系统，如线性弹性的Lame方程。

The solvability theory for complex valued elliptic PDEs and systems is significantly less understood than the equivalent scalar elliptic theory with real coefficients. This is due to the lack of certain tools available in the scalar real case such as themaximum principle or the De Giorgi-Nash-Moser regularity theory. Recently as new concept called p-ellipticity has allowed to make significant progress in the setting of elliptic complex valued PDEs. The aim of the project is to further explore this breakthrough and its consequences to solvability of such PDEs under the Regularity/Neumann boundary conditions and questions of extrapolation of solvability. The second topic the project will look at is p-ellipticity for elliptic systems withparticular focus on specific systems such as the Lame equations for linear elasticity.