Research Projects

The basic goal of the project is to develop a nonlinear potential theory for quasilinear systems of vector-valued differential forms, which generalises both the p-Laplace equation, p-Laplacian system and the p-curl curl operator that appears in the context of electromagnetism and fluid mechanics. Such theory for p-Laplace equation is well-developed and is being actively developed for the p-Laplacian systems. But these methods can not be applied either to the p-curl curl operator or the general case of vector-valued forms. The plan is to develop methods that is adapted to the exterior algebra structure and can handle the additional difficulties created by the non-ellipticity of the operators.