1:00 pm Friday, March 9, 2007
Sophex: Properties of Fractional Sobolev Spaces by Eric Baer (UT-Austin) in RLM 9.166
On a set of measure zero, the value of an arbitrary function is undefined. As a result incorporating boundary conditions into the definition of a generalized solution of a PDE becomes difficult. One way to resolve this issue is to define a "trace operator" on the Sobolev space $W^(1,p)$. The image of $W^(1,p)$ under this trace operator is then a fractional Sobolev space. After providing the relevant definitions, I will discuss an interesting characterization of $W^(1,p)$ due to Bourgain, Brezis and Mironescu. Submitted by
|
|