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Nonlinear potential theory on metric spaces

Nonlinear potential theory on metric spaces
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Field name Details
Dewey Class 514.325 (DDC 23.)
Title Nonlinear potential theory on metric spaces (M) / Anders Björn, Jana Björn
Author Björn, Anders
Added Personal Name Björn, Jana
Publication Zürich, Switzerland : European Mathematical Society , 2011
Physical Details xii, 403 pages : ill. ; 25 cm
Series EMS Tracts in mathematics ; 17
ISBN 9783037190999
Summary Note The p-Laplace equation is the main prototype for nonlinear elliptic problems and forms a basis for various applications, such as injection moulding of plastics, nonlinear elasticity theory, and image processing. Its solutions, called p-harmonic functions, have been studied in various contexts since the 1960s, first on Euclidean spaces and later on Riemannian manifolds, graphs, and Heisenberg groups. Nonlinear potential theory of p-harmonic functions on metric spaces has been developing since the 1990s and generalizes and unites these earlier theories.This monograph gives a unified treatment of the subject and covers most of the available results in the field, so far scattered over a large number of research papers. The aim is to serve both as an introduction to the area for interested readers and as a reference text for active researchers. The presentation is rather self contained, but it is assumed that readers know measure theory and functional analysis.The first half of the book deals with Sobolev type spaces, so-called Newtonian spaces, based on upper gradients on general metric spaces. In the second half, these spaces are used to study p-harmonic functions on metric spaces, and a nonlinear potential theory is developed under some additional, but natural, assumptions on the underlying metric space. Each chapter contains historical notes with relevant references, and an extensive index is provided at the end of the book.:
Contents note Newtonian spaces -- Minimal p-weak upper gradients -- Doubling measures -- Poincaré inequalities -- Properties of Newtonian functions -- Capacities -- Superminimizers -- Interior regularity -- Superharmonic functions -- The Dirichlet problem for p-harmonic functions -- Boundary regularity -- Removable singularities -- Irregular boundary points -- Regular sets and applications thereof.
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Barcode Shelf Location Collection Volume Ref. Branch Status Due Date
0000000044264 515.12 BJO
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