Existence of solutions for semi-linear degenerate elliptic equations

    This talk concerns Dirichlet problems for semi-linear degenerate equations. Degenerate elliptic operators are motivated by the structure of the corresponding singular manifolds. Here we will first discuss the definitions of the degenerate elliptic operators, and then the weighted Sobolev spaces.
    Some inequalities will also be introduced, which are useful for the proof of the existence of solutions for the corresponding semi-linear degenerate equations.