New Questions Related to the Topological Degree

@inproceedings{Brezis2006NewQR,
  title={New Questions Related to the Topological Degree},
  author={H. Brezis},
  year={2006}
}
  • H. Brezis
  • Published 2006
  • Mathematics
  • 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… CONTINUE READING
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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 35 REFERENCES
    Topology of sobolev mappings, II
    • 97
    • PDF
    On a question of Brézis and Nirenberg concerning the degree of circle maps
    • 11
    A new estimate for the topological degree
    • 27
    • Highly Influential
    • PDF
    Harmonic maps with defects
    • 422
    • PDF
    Ginzburg-Landau Vortices
    • 722
    Degree theory and BMO; part II: Compact manifolds with boundaries
    • 213
    • Highly Influential
    • PDF
    A boundary value problem related to the Ginzburg-Landau model
    • 79
    Large solutions for harmonic maps in two dimensions
    • 121
    • PDF
    Degree Theory: Old and New
    • 22
    • PDF