With The Symmetry Group Variational Structure Of Partial Differential Equations, Variational Identities

Variational identity play a important role to prove nonexistence and get prior estimate of solution, In this thesis, we study following parts on the relationship of symmetry group of partial differential equations with variational structure and the variational identity. In chapter 1, we review the background and the historical facts of variational identity. In chapter 2, the foundation method is introduced in detail. In chapter 3, we have proved that the Pucci and Serrin's general identity is a special Noether's identity and get various identity by computing the symmetry group of equation. In chapter 4, we compute the symmetry group, variational symmetry group, divergence symmetry group of some operator equation. As some application we obtain various identity of equation in chapter 5. In the appendix we get the methods of construct nonstarshaped domain.