Potential analysis of various function spaces and application

偏微分方程理论是运用数学方法研究自然界中各种现象的重要数学工具。要做到这一点，我们的第一个任务是找到一个合适的描述一种现象的偏微分方程，并分析方程的解，然后我们可以预测我们不久的将来。为此，功能空间扮演着重要的角色。在我们的研究中，我们扩展了Sobolev的著名理论，并研究了大量的现象作为应用。人们期望它能进一步发展我们的人类福利理论。

To develop various phenomena surrounding our nature by applying Mathematical method, a theory of partial differential equation is a crucial mathematical tool. To do so, our first task is to find a suitable partial differential equation describing a phenomenon and analyze a solution of the equation, and then we can predict our near future. For this purpose, function spaces play an important role.In our study, we extend the famous theory developed by Sobolev and investigate tremendous phenomena as applications. It will be expected to give further development of our theory for human welfare.