Research on the regularity of solutions for nonlinear partial differential equations related to variational problems

点击翻译按钮获取中文摘要

The problems to find maps or functions that give critical points of a quantity under consideration are called variational problems. When we treat variational problems, we often employ the following 2-step procedure: first, we find a "solution" in the class of maps that are differentiable in certain generalized sense, and, as the second step, we prove that the "solution" is appropriately smooth. This second step is called "regularity problem", and in this research we treat "regularity problem". In general, when we consider "regularity problem", we often assume continuity or, more strongly, differentiability of coefficients. In this research, we tried to obtain some regularity results under weaker conditions on the smoothness of coefficients, and we have gotten some new results.