The Symmetry Of The Partial Differential Equation Under The Overdetermined Boundary Condition

There are many methods for the symmetry study of the overdetermined equation boundary value problem, for example, the moving plane method, Steiner symmetrization, domain derivative, geometry. In this paper, we use the classical moving plane method to investigate the symmetry of two kinds of overdetermined boundary value problems.In Chapter 1, we present some preliminaries.In Chapter 2, we investigate the symmetry of the solution and domain for a class of Laplace type overdetermined boundary value problem and obtain the sufficient condition for the symmetry of the solution and the domain.In Chapter 3, we present some research about the symmetry of the positive solution which has only one critical point for a class of non-homogeneous A-Laplace type overdetermined boundary value problem and obtain the sufficient condition for the symmetry of this kind of boundary problem.