Existence and regularity theory in weighted Sobolev spaces and applications

My emphasis in this thesis is to contribute to the solvability and uniqueness of solutions to the nonhomogenous boundary value problems of elliptic type, dealing with degenerate PDEs. My aim is to consider possibly general class of weights. In particular, I consider the $B_{p}$-class of weights which is much more general class than the commonly studied Muckenhoupt $A_{p}$-class. I adapt the general functional analytical tools, like, Baire method, Minty-Brouder Theorem, Lax-Miligram Theorem, Ekeland's Variational Principle, to the setting of degenerate PDEs