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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Sobolev Maps to the Circle: From the Perspective of Analysis, Geometry, and Topology

Sobolev Maps to the Circle: From the Perspective of Analysis, Geometry, and Topology

Mironescu, Petru
Brezis, Haim

Hardcover

Series: Progress in Nonlinear Differential Equations and Their Appli, Book 96

General Mathematics

ISBN10: 1071615106
ISBN13: 9781071615102
Publisher: Birkhauser
Published: Dec 2 2021
Pages: 530
Weight: 2.12
Height: 1.25 Width: 6.14 Depth: 9.21
Language: English
The theory of real-valued Sobolev functions is a classical part of analysis and has a wide range of applications in pure and applied mathematics. By contrast, the study of manifold-valued Sobolev maps is relatively new. The incentive to explore these spaces arose in the last forty years from geometry and physics. This monograph is the first to provide a unified, comprehensive treatment of Sobolev maps to the circle, presenting numerous results obtained by the authors and others. Many surprising connections to other areas of mathematics are explored, including the Monge-Kantorovich theory in optimal transport, items in geometric measure theory, Fourier series, and non-local functionals occurring, for example, as denoising filters in image processing. Numerous digressions provide a glimpse of the theory of sphere-valued Sobolev maps.

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