Mathematical Sciences: Sobolev Estimates for Weighted OrliczSpaces and their Applications to Linear and Nonlinear Boundary Value Problems

点击翻译按钮获取中文摘要

This project will focus on the development of inequalities which provide information on the embedding of Orlicz spaces of the weighted Sobolev type into other Orlicz spaces. Included will be studies of embedding of weighted Sobolev spaces into weighted Lebesque spaces. Basic tools involved in this work are singular integral operators, capacity theory and maximal operators. Applications will be made to nonlinear partial differential equations such as semilinear elliptic boundary value problems.