Lebesgue and Sobolev Spaces with Variable Exponents by Lars Diening (PDF)

Description

1 Introduction.- 2 A framework for function spaces.- 3 Variable exponent Lebesgue spaces.- 4 The maximal operator.- 5 The generalized Muckenhoupt condition*.- 6 Classical operators.- 7 Transfer techniques.- 8 Introduction to Sobolev spaces.- 9. Density of regular functions.- 10. Capacities.- 11 Fine properties of Sobolev functions.- 12 Other spaces of differentiable functions.- 13 Dirichlet energy integral and Laplace equation.- 14 PDEs and fluid dynamics

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⭐仕事先の図書館で借りて読んでいましたが，頻繁に参照するので，手元に置いておきたかった本です．発注後すぐに手元に届きましたので重宝しています．

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