Nonlocal Korn-type characterization of Sobolev vector fields. (English) Zbl 1250.46021
Summary: A new nonlocal characterization of Sobolev vector fields in the spirit of Korn’s inequality is obtained. As an application of this result, a nonlocal means of identification of rigid motions is given. A nonlocal characterization of vector fields with bounded deformation is also presented. A compactness criteria is proved for bounded sequences of vector fields in \(L^p\).
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 46E40 | Spaces of vector- and operator-valued functions |
| 45A05 | Linear integral equations |
References:
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