liu.seSök publikationer i DiVA
Ändra sökning
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Nonlinear Potential Theory on Metric Spaces
Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.ORCID-id: 0000-0002-9677-8321
Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.ORCID-id: 0000-0002-1238-6751
2011 (Engelska)Bok (Refereegranskat)
Abstract [en]

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 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.

Ort, förlag, år, upplaga, sidor
Zurich: European Mathematical Society , 2011, 1. , s. 403
Serie
EMS Tracts in Mathematics ; 17
Nyckelord [en]
Metric spaces, Harmonic functions, Potential theory (Mathematics)
Nyckelord [sv]
Potentialteori, Topologi
Nationell ämneskategori
Matematisk analys
Identifikatorer
URN: urn:nbn:se:liu:diva-72620DOI: 10.4171/099ISBN: 978-3-03719-099-9 (tryckt)OAI: oai:DiVA.org:liu-72620DiVA, id: diva2:460712
Tillgänglig från: 2011-12-01 Skapad: 2011-12-01 Senast uppdaterad: 2016-05-04Bibliografiskt granskad

Open Access i DiVA

Fulltext saknas i DiVA

Övriga länkar

Förlagets fulltextFind book in another country/Hitta boken i ett annat landfind book at a swedish library/hitta boken i ett svenskt bibliotek

Personposter BETA

Björn, AndersBjörn, Jana

Sök vidare i DiVA

Av författaren/redaktören
Björn, AndersBjörn, Jana
Av organisationen
Tillämpad matematikTekniska högskolan
Matematisk analys

Sök vidare utanför DiVA

GoogleGoogle Scholar

doi
isbn
urn-nbn

Altmetricpoäng

doi
isbn
urn-nbn
Totalt: 173 träffar
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf