ABSTRACT
The analysis of PDE’s naturally involves function spaces that are not only defined in terms of the properties of the function itself, but also in terms of the properties of its derivatives. Sobolev spaces prove to be useful tools in this analysis. For a comprehensive study we refer to Adams [1]. Sobolev spaces are Banach spaces by construction, and the new feature is that in order for a function to belong to a certain Sobolev space, both the function itself and its derivatives, up to a certain order, must lie in a certain Lp- space. Since we do not attempt to give anything but a brief introduction to the subject, we will assume that the boundaries of the domains in Rn we consider are all smooth. Sobolev spaces in nonsmooth domains are studied in detail in Grisvard [7].
