A Class Of Boundary Value Problems For ?₂-Yamabe Equation

Yamabe problem is an important problem of nonlinear partial differential e-quation in geometry and analysis.And the ?k-Yamabe equation about ?k-Yamabe operator is a class of the fully nonlinear partial differential equation,which is the generalization of the classical Yamabe equation.The research of this equation is of great value to the development of fully nonlinear partial differential equationsIn this thesis,we mainly study the homogeneous boundary value problem of?2-Yamabe equation and attempt to generalize the Brezis-Nirenberg problem about semilinear Yamabe equation of Laplace operator to the fully nonlinear ?2-Yamabe equation.Under the condition of the existence of upper and lower solutions,by constructing appropriate barrier function and using the maximum principle,we establish global second order derivative estimate for the homogeneous boundary value problem of ?2-Yamabe equation.