Chian Chuah
The Ohio State University
Title
Measurement of non-compactness of Sobolev embedding into function spaces
Abstract
The study of Sobolev embedding into function spaces such as the Lebesgue spaces and Lorentz spaces plays a fundamental role in the field of PDE and approximation theory. In the classical setting, the Rellich–Kondrachov theorem provides condition on which the Sobolev embedding is compact. In the case where the embedding is non-compact, there are various levels to which one can measure the quality of non-compactness. In this talk, we discuss the compactness of Sobolev embedding into the variable Lorentz space where the behavior of non-compactness is concentrated around a single point. The quality of non-compactness is also discussed in this case. If time permits, we also discuss the measurement of non-compactness for various function spaces. This is a joint work with Jan Lang and Liding Yao.
