Estimates for the topological degree and related topics. (English) Zbl 1321.46037
Summary: This is a survey paper on estimates for the topological degree and related topics which range from the characterizations of Sobolev spaces and BV functions to the Jacobian determinant and nonlocal filter problems in Image Processing. These results are obtained jointly with Bourgain and Brezis. Several open questions are mentioned.
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 55M25 | Degree, winding number |
| 49J99 | Existence theories in calculus of variations and optimal control |
| 46B50 | Compactness in Banach (or normed) spaces |
| 26B10 | Implicit function theorems, Jacobians, transformations with several variables |
| 47H11 | Degree theory for nonlinear operators |
| 46-02 | Research exposition (monographs, survey articles) pertaining to functional analysis |
Keywords:
topological degree; Sobolev spaces; gamma-convergence; distributional Jacobian; determinant; image processingReferences:
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