The analysis and geometry of Hardy's inequality / Alexander A Balinsky, W. Desmond Evans, Roger T. Lewis.

Format:

Book

Author/Creator:

Balinsky, A. A. (Alexander A.), author.

Evans, W. D. (William Desmond), author.

Lewis, Roger T., author.

Series:

Universitext

Universitext, 0172-5939

Language:

English

Subjects (All):

Inequalities (Mathematics).

Physical Description:

xv, 263 pages : illustrations ; 24 cm.

Place of Publication:

Cham : Springer, [2015]

Summary:

This volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics. The inequality and its extensions and refinements are not only of intrinsic interest but are indispensable tools in many areas of mathematics and mathematical physics. Hardy inequalities on domains have a substantial role and this necessitates a detailed investigation of significant geometric properties of a domain and its boundary. Other topics covered in this volume are Hardy- Sobolev-Maz'ya inequalities; inequalities of Hardy-type involving magnetic fields; Hardy, Sobolev and Cwikel-Lieb-Rosenbljum inequalities for Pauli operators; the Rellich inequality. The Analysis and Geometry of Hardy's Inequality provides an up-to-date account of research in areas of contemporary interest and would be suitable for a graduate course in mathematics or physics. A good basic knowledge of real and complex analysis is a prerequisite.

Contents:

Hardy, Sobolev, and CLR inequalities

Boundary curvatures and the distance function

Hardy's inequality on domains

Hardy, Sobolev, Maz'ya (HSM) inequalities

Inequalities and operators involving magnetic elds

The Rellich inequality.

Notes:

Includes bibliographical references (pages 251-256) and indexes.

ISBN:

3319228692

9783319228693

OCLC:

913767445