Sobolev Spaces: With Applications to Elliptic Partial Differential Equations (Hardcover, 2, Revised, Augmen)

Introduction.- 1 .Basic Properties of Sobolev Spaces.- 2 .Inequalities for Functions Vanishing at the Boundary.- 3.Conductor and Capacitary Inequalities with Applications to Sobolev-type Embeddings.- 4.Generalizations for Functions on Manifolds and Topological Spaces.- 5.Integrability of Functions in the Space L 1/1(_).- 6.Integrability of Functions in the Space L 1/p (_).- 7.Continuity and Boundedness of Functions in Sobolev Spaces.- 8.Localization Moduli of Sobolev Embeddings for General Domains.- 9.Space of Functions of Bounded Variation.- 10.Certain Function Spaces, Capacities and Potentials.- 11 Capacitary and Trace Inequalities for Functions in Rn with Derivatives of an Arbitrary Order.-12.Pointwise Interpolation Inequalities for Derivatives and Potentials.- 13.A Variant of Capacity.- 14.-Integral Inequality for Functions on a Cube.- 15.Embedding of the Space L l/p(_) into Other Function Spaces.- 16.Embedding L l/p(_) _ W m/r(_).-17.Approximation in Weighted Sobolev Spaces.-18.Spectrum of the Schrodinger operator and the Dirichlet Laplacian.- References.- List of Symbols.- Subject Index.- Author Index.