Noncompactness of a Sobolev embedding by translation

Translations of one compactly supported bump have equal Sobolev norms. Widely separated translates have disjoint supports and remain a fixed positive distance apart in

L^{2}

, obstructing compactness on an unbounded domain.

Table of contents 92 2
- Loss of compactness at infinity Noncompactness of a Sobolev embedding by translation 25
- Vanishing Dirichlet energy by dilation on the line Noncompactness of a Sobolev embedding by translation 35

 Ancestors (7)

Sobolev embedding theorem
Sobolev space
Functional analysis
Analysis
Area of mathematics
Mathematics
 Home

 Incoming links (1)

Solution