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- W36295492 abstract "Degree theory for continuous maps has a long history and has been extensively studied, both from the point of view of analysis and topology. If f ∈ C 0(S n, S n), deg f is a well-defined element of ℤ, which is stable under continuous deformation. Starting in the early 1980s, the need to define a degree for some classes of discontinuous maps emerged from the study of some nonlinear PDEs (related to problems in liquid crystals and superconductors). These examples involved Sobolev maps in the limiting case of the Sobolev embedding; see Sections 2 and 3 below. (Topological questions for Sobolev maps strictly below the limiting exponent have been investigated in [15] and [14].) In these cases, the Sobolev embedding asserts only that such maps belong to the space VMO (see below) and need not be continuous." @default.
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- W36295492 date "2007-05-30" @default.
- W36295492 modified "2023-10-18" @default.
- W36295492 title "New Questions Related to the Topological Degree" @default.
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- W36295492 doi "https://doi.org/10.1007/0-8176-4467-9_3" @default.
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