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

寻找给出所考虑的量的临界点的映射或函数的问题称为变分问题。当我们处理变分问题时，我们经常采用以下两步程序：首先，我们在某些广义意义下可微的映射类中找到一个“解”，作为第二步，我们证明“解”是适当光滑的。这第二步被称为“正则性问题”，在本研究中，我们处理“正则性问题”。一般来说，当我们考虑“正则性问题”时，我们经常假设系数的连续性或更强的可微性。在本研究中，我们试图在较弱的条件下得到一些关于系数光滑性的正则性结果，并得到了一些新的结果。

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.