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001			141-111105
003			CH-001817-3
005			20170613140804.0
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007			cr nn mmmmamaa
008			111105e20111105sz fot ||| 0|eng d
020			_a9783037195994
024	7	0	_a10.4171/099 _2doi
040			_ach0018173
072		7	_aPBK _2bicssc
084			_a31-xx _2msc
100	1		_aBjörn, Anders, _eauthor.
245	1	0	_aNonlinear Potential Theory on Metric Spaces _h[electronic resource] / _cAnders Björn, Jana Björn
260	3		_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2011
264		1	_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2011
300			_a1 online resource (415 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	0		_aEMS Tracts in Mathematics (ETM) _v17
506	1		_aRestricted to subscribers: _uhttp://www.ems-ph.org/ebooks.php
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	7	_aCalculus & mathematical analysis _2bicssc
650	0	7	_aPotential theory _2msc
700	1		_aBjörn, Anders, _eauthor.
700	1		_aBjörn, Jana, _eauthor.
856	4	0	_uhttps://doi.org/10.4171/099
856	4	2	_3cover image _uhttp://www.ems-ph.org/img/books/björn_mini.jpg
942			_2EBK13816 _cEBK
999			_c50440 _d50440