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

这个项目将集中于发展关于加权Sobolev型Orlicz空间到其他Orlicz空间的嵌入的信息的不等式。其中包括加权Sobolev空间到加权Lebesque空间的嵌入的研究。本文所涉及的基本工具是奇异积分算子、容量理论和极大算子。应用于非线性偏微分方程，如半线性椭圆型边值问题。

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.