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101 0 $aeng
135   $aurnn#mmmmamaa
181   $ctxt$2rdacontent
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200 10$aElliptic PDEs, measures and capacities$b[electronic resource] $efrom the Poisson equation to nonlinear Thomas-Fermi problems /$fAugusto C. Ponce
210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2016
215   $a1 online resource (463 pages)
225 0 $aEMS Tracts in Mathematics (ETM)$v23
311   $a3-03719-140-6 
330   $aWinner of the 2014 EMS Monograph Award!  Partial differential equations (PDEs) and geometric measure theory (GMT) are branches of analysis whose connections are usually not emphasized in introductory graduate courses. Yet, one cannot dissociate the notions of mass or electric charge, naturally described in terms of measures, from the physical potential they generate. Having such a principle in mind, this book illustrates the beautiful interplay between tools from PDEs and GMT in a simple and elegant way by investigating properties like existence and regularity of solutions of linear and nonlinear elliptic PDEs.  Inspired by a variety of sources, from the pioneer balayage scheme of Poincare? to more recent results related to the Thomas-Fermi and the Chern-Simons models, the problems covered in this book follow an original presentation, intended to emphasize the main ideas in the proofs. Classical techniques like regularity theory, maximum principles and the method of sub- and supersolutions are adapted to the setting where merely integrability or density assumptions on the data are available. The distinguished role played by capacities and precise representatives is also explained.  Other special features are:  ? the remarkable equivalence between Sobolev capacities and Hausdorff contents in terms of trace inequalities;  ? the strong approximation of measures in terms of capacities or densities, normally absent from GMT books;  ? the rescue of the strong maximum principle for the Schro?dinger operator involving singular potentials.  This book invites the reader to a trip through modern techniques in the frontier of elliptic PDEs and GMT, and is addressed to graduate students and researchers having some deep interest in analysis. Most of the chapters can be read independently, and only basic knowledge of measure theory, functional analysis and Sobolev spaces is required.
606   $aCalculus & mathematical analysis$2bicssc
606   $aMeasure and integration$2msc
606   $aPotential theory$2msc
615 07$aCalculus & mathematical analysis
615 07$aMeasure and integration
615 07$aPotential theory
676   $a515/.3533
686   $a28-xx$a31-xx$2msc
700   $aPonce$b Augusto C.$01071024
801  0$bch0018173
906   $aBOOK
912   $a9910153279203321
996   $aElliptic PDEs, Measures and Capacities$92565671
997   $aUNINA