Title: Sobolev spaces : with applications to elliptic partial differential equations /
Authors: Mazʹi͡a, V. G.; Shaposhnikova, T. O.
Publisher: Springer Verlag,
Year: 2011
Subjects: Sobolev spaces.; Mathematics; Global analysis (Mathematics).
Contents: Basic Properties of Sobolev Spaces -- Inequalities for Functions Vanishing at the Boundary -- Conductor and Capacitary Inequalities with Applications to Sobolev-Type Embeddings -- Generalizations for Functions on Manifolds and Topological Spaces -- Integrability of Functions in the Space L [superscript 1] [subscript 1] [omega] -- Integrability of Functions in the Space L [superscript 1] [subscript p] [omega] -- Continuity and Boundedness of Functions in Sobolev Spaces -- Localization Moduli of Sobolev Embeddings for General Domains -- Space of Functions of Bounded Variation -- Certain Function Spaces, Capacities, and Potentials -- Capacitary and Trace Inequalities for Functions in R [superscript n] with Derivatives of an Arbitrary Order -- Pointwise Interpolation Inequalities for Derivatives and Potentials -- A Variant of Capacity -- Integral Inequality for Functions on a Cube -- Embedding of the Space L̊[superscript l] [subscript p] [omega] into Other Function Spaces -- Embedding L̊[superscript l] [subscript p] [omega],[nu] [subset of] W[superscript m] [subscript r] [omega] -- Approximation in Weighted Sobolev Spaces -- Spectrum of the Schrödinger Operator and the Dirichlet Laplacian.