[Home]
[
News]
[ Events]
[ People]
[ Research]
[ Education]
[Visitor Info]
[UCSD Only]
[Admin]
Pointwise Multiplication in Bessel Potential Spaces and
Sobolev-Slobodeckij Spaces
Ali Behzadan
UCSD
Abstract:
Let $f \in W^{s1,p1}$ and $g \in W^{s2,p2}$ ($s1,s2\ge 0)$. What can be said about $fg$? To which Sobolev spaces does the product $fg$ belong? This is the question that we want to talk about. Why do we care about this question? As we will discuss, one of the main applications of such results is in the theory of partial differential equations (PDEs) and in particular nonlinear elliptic PDEs. We will review some of the well-known results and present alternate proofs of those results. In particular we will point out a common mistake in some of the existing literature as we discuss the question of existence of Holder-type inequalities for the product of two functions in Sobolev spaces.
Tuesday, November 18, 2014
11:00AM AP&M 2402
News]
[ Events]
[ People]
[ Research]
[ Education]
[Visitor Info]
[UCSD Only]
[Admin]
Directors:
Randolph E. Bank
Philip E. Gill
Michael Holst
Administrative Contact:
[ Click to Send Email ]
Randolph E. Bank
Philip E. Gill
Michael Holst
Administrative Contact:
[ Click to Send Email ]
Ali Behzadan
UCSD
Abstract:
Let $f \in W^{s1,p1}$ and $g \in W^{s2,p2}$ ($s1,s2\ge 0)$. What can be said about $fg$? To which Sobolev spaces does the product $fg$ belong? This is the question that we want to talk about. Why do we care about this question? As we will discuss, one of the main applications of such results is in the theory of partial differential equations (PDEs) and in particular nonlinear elliptic PDEs. We will review some of the well-known results and present alternate proofs of those results. In particular we will point out a common mistake in some of the existing literature as we discuss the question of existence of Holder-type inequalities for the product of two functions in Sobolev spaces.
Tuesday, November 18, 2014
11:00AM AP&M 2402