On a Review of the Sobolev Space
Eziokwu, C. Emmanuel *
Department of Mathematics, College of Physical and Applied Sciences, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Sobolev, an aspect of Functional Analysis has since the middle of nineteenth century been very useful in many areas of pure mathematics such as Ordinary Differential Equation, Numerical Analysis etc. and now developed into what is known as Sobolev Space. Due to its growing relevance in analytical mathematics, this review paper becomes important in that it displays exciting theoretic definitions and results in the Sobolev Space with impressive details on the Real Index, integration by part, special inequalities and the Embedding Theorem, while towards the end of the work was conclusion in the form of a mathematical remark.
Keywords: Fabry disease, Sobolev space, Uptake of α-galactosidase, norm and Hilbert space, Lysosomal enzymes, Friedrich and Poincare inequalities, the embedding theorem.