Paper Info
Title
Trace Theorems for some Nonlocal Function Spaces with Heterogeneous Localization.
Abstract
It is a classical result of Sobolev spaces that any H-1 function has a well-defined H-1/2 trace on the boundary of a sufficient regular domain. In this work, we present stronger and more general versions of such a trace theorem in a new nonlocal function space S(Omega) satisfying H-1(Omega) subset of S(Omega) subset of L-2(Omega). The new space S (Omega) is associated with a nonlocal norm characterized by a nonlocal interaction kernel that is de fined heterogeneously with a special localization feature on the boundary. Through the heterogeneous localization, we are able to show that the H-1/2 norm of the trace on the boundary can be controlled by the nonlocal norm that is weaker than the classical H-1 norm. In fact, the trace theorems can be essentially shown without imposing any extra regularity of the function in the interior of the domain other than being square integrable. Implications of the new trace theorems for the coupling of local and nonlocal equations and possible further generalizations are also discussed.
Year
DOI
Venue
2017
10.1137/16M1078811
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Keywords
Field
DocType
nonlocal operator,nonlocal function space,trace map,trace inequality,Hardy inequality,heterogeneous localization,vanishing horizon
Kernel (linear algebra),Discrete mathematics,Function space,Square-integrable function,Coupling,Mathematical analysis,Sobolev space,Omega,Mathematics
Journal
Volume
Issue
ISSN
49
2
0036-1410
Citations 
PageRank 
References 
2
0.44
2
Authors
2
Name
Order
Citations
PageRank
Xiaochuan Tian1143.01
Qiang Du21692188.27