Titlebook: Weakly Differentiable Functions; Sobolev Spaces and F William P. Ziemer Textbook 1989 Springer Science+Business Media New York 1989 Derivat

adhesive

微生物

Sobolev Spaces and Their Basic Properties,e basic Sobolev inequality is proved in two ways, one of which employs the co-area formula (Section 2.7) to obtain the best constant in the inequality. This method relates the Sobolev inequality to the isoperimetric inequality.

Granular

外面

Preliminaries, information contained in this chapter will be well-known by the reader and therefore no attempt has been made to make a complete and thorough presentation. Rather, we merely introduce notation and develop a few concepts that will be needed in the sequel.

myalgia

acrophobia

LATER

Pointwise Behavior of Sobolev Functions,tributional derivatives of . belong to .(Ω), it is therefore natural to inquire whether the function . possesses some type of regularity (smoothness) in the classical sense. The main purpose of this chapter is to show that this question can be answered in the affirmative if interpreted appropriately

得意人

Functions of Bounded Variation,ned measure with finite total variation. This chapter is directed to the multivariate analog of these functions, namely the class of .functions whose partial derivatives are measures in the sense of distributions. Just as absolutely continuous functions form a subclass of BV functions, so it is that

incubus

Textbook 1989ves in the sense of distributions are either LP functions or (signed) measures with finite total variation. The former class of functions comprises what is now known as Sobolev spaces, though its origin, traceable to the early 1900s, predates the contributions by Sobolev. Both classes of functions,

hardheaded