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Sobolev met Poincaré

2000; American Mathematical Society; Volume: 145; Issue: 688 Linguagem: Inglês

10.1090/memo/0688

1947-6221

Piotr Hajłasz, Pekka Koskela,

Historical and Contemporary Political Dynamics

Introduction What are Poincare and Sobolev inequalities? Poincare inequalities, pointwise estimates, and Sobolev classes Examples and necessary conditions Sobolev type inequalities by means of Riesz potentials Trudinger inequality A version of the Sobolev embedding theorem on spheres Rellich-Kondrachov Sobolev classes in John domains Poincare inequality: examples Carnot-Caratheodory spaces Graphs Applications to PDE and nonlinear potential theory Appendix References.