 Pokhozhaev's identity

Pokhozhaev's identity is a mathematical result related to the study of certain partial differential equations, particularly in the context of nonlinear analysis and the theory of elliptic equations. It provides a relationship that can be used to derive energy estimates and to study the qualitative properties of solutions to nonlinear equations. The identity is often stated in the context of solutions to the boundary value problems for nonlinear elliptic equations and is used to establish properties such as symmetry, monotonicity, or the uniqueness of solutions.