Sobolev-Poincaré implies John

Stephen M. Buckley; Pekka Koskela

doi:10.4310/mrl.1995.v2.n5.a5

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Sobolev-Poincaré implies John

Stephen M. Buckley Pekka Koskela

Year: 1995 Journal: Mathematical Research Letters Vol: 2 (5)Pages: 577-593 Publisher: International Press of Boston

DOI: 10.4310/mrl.1995.v2.n5.a5

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Abstract

We establish necessary conditions for the validity of Sobolev-Poincaré type inequalities. We give a geometric characterisation for the validity of this inequality for simply connected plane domains.

Keywords:

Mathematics Sobolev space Poincaré conjecture Pure mathematics

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Analytic and geometric function theory

Physical Sciences → Mathematics → Geometry and Topology

Nonlinear Partial Differential Equations

Physical Sciences → Mathematics → Applied Mathematics

Differential Equations and Boundary Problems

Physical Sciences → Mathematics → Applied Mathematics

Sobolev-Poincaré implies John

Abstract

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