Potential analysis of various function spaces and application

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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.