MARC Record from marc_columbia

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035 $a(OCoLC)ocn768398561
035 $a(NNC)16056823
040 $aCOO$beng$erda$cCOO$dOKU$dOCLCQ$dOSU$dOCLCO$dOCLCQ$dOCLCF$dNOC$dLLB$dSTF$dN$T$dINT$dOCLCQ$dOCLCO
019 $a817964895
020 $a9783037195994$q(electronic bk.)
020 $a3037195991$q(electronic bk.)
020 $z9783037190999
020 $z303719099X
024 70 $a10.4171/099$2doi
035 $a(OCoLC)768398561$z(OCoLC)817964895
050 4 $aQA611.28$b.B59 2011eb
072 7 $aPBK$2bicssc
072 7 $aMAT$x038000$2bisacsh
082 04 $a514/.325$223
084 $a31-xx$2msc
049 $aZCUA
100 1 $aBjörn, Anders,$d1966-$eauthor.
245 10 $aNonlinear potential theory on metric spaces /$cAnders Björn, Jana Björn.
264 1 $aZürich, Switzerland :$bEuropean Mathematical Society,$c[2011]
264 4 $c©2011
300 $a1 online resource (xii, 403 pages) :$billustrations.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
490 1 $aEMS tracts in mathematics ;$v17
504 $aIncludes bibliographical references (pages 369-388) and index.
505 0 $aNewtonian 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.
588 $aDescription based on print version record.
520 $aThe 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 an interested reader and as a reference text for an active researcher. The presentation is rather self-contained, but the reader is assumed to 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.
650 0 $aMetric spaces.
650 0 $aHarmonic functions.
650 0 $aPotential theory (Mathematics)
650 6 $aEspaces métriques.
650 6 $aFonctions harmoniques.
650 6 $aThéorie du potentiel.
650 07 $aCalculus & mathematical analysis.$2bicssc
650 7 $aMATHEMATICS / Topology$2bisacsh
650 7 $aHarmonic functions.$2fast$0(OCoLC)fst00951500
650 7 $aMetric spaces.$2fast$0(OCoLC)fst01018813
650 7 $aPotential theory (Mathematics)$2fast$0(OCoLC)fst01073489
650 07 $aPotential theory.$2msc
655 4 $aElectronic books.
700 1 $aBjörn, Jana,$eauthor.
700 1 $aBjörn, Jana.
776 08 $iPrint version:$aBjörn, Anders, 1966-$tNonlinear potential theory on metric spaces.$dZürich, Switzerland : European Mathematical Society, ©2011$z9783037190999$w(DLC) 2012359355$w(OCoLC)775469296
830 0 $aEMS tracts in mathematics ;$v17.
856 40 $uhttp://www.columbia.edu/cgi-bin/cul/resolve?clio16056823$zAll EBSCO eBooks
852 8 $blweb$hEBOOKS