Homogenization Of A Class Of Degenerate Elliptic And Parabolic Equations

The homogenization of a class of nonlinear degenerate elliptic problems and a class of nonlinear degenerate parabolic problems is studied in this dissertation.Two powerful classical methods in theory of homogenization are De Giorgi's variational convergence method and L.Tartar's energy method. For the homogenization of the partial differential equations with periodical coefficients,in 1989,Nguetseng proposed a new method, i.e.,the so–called two-scale convergence method, which exploits fully the periodicity of coefficients.Using L.Tartar's energy method and some techniques from harmonic analysis, such as The Muckenhoupt class for a suitable constant (see definition below), Weighted Sobolev space and so on, we obtain the homogenized results of the following degenerate elliptic problems and degenerate parabolic problems:(一).(二). These results extend the known results existing in the literature.