LEADER 02729nam 22003975a 450 001 9910151928503321 005 20111105234510.0 010 $a3-03719-599-1 024 70$a10.4171/099 035 $a(CKB)3710000000953873 035 $a(CH-001817-3)141-111105 035 $a(PPN)178156000 035 $a(EXLCZ)993710000000953873 100 $a20111105j20111105 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNonlinear Potential Theory on Metric Spaces$b[electronic resource] /$fAnders Bjo?rn, Jana Bjo?rn 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2011 215 $a1 online resource (415 pages) 225 0 $aEMS Tracts in Mathematics (ETM)$v17 330 $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. 606 $aCalculus & mathematical analysis$2bicssc 606 $aPotential theory$2msc 615 07$aCalculus & mathematical analysis 615 07$aPotential theory 686 $a31-xx$2msc 700 $aBjo?rn$b Anders$01071046 702 $aBjo?rn$b Jana 801 0$bch0018173 906 $aBOOK 912 $a9910151928503321 996 $aNonlinear Potential Theory on Metric Spaces$92565743 997 $aUNINA