Elliptic Regularity Theory A First Course
These lecture notes provide a self-contained introduction to regularity theory for elliptic equations and systems in divergence form. After a short review of some classical results on everywhere regularity for scalar-valued weak solutions, the presentatio
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Lisa Beck
Elliptic Regularity Theory A First Course
Lecture Notes of the Unione Matematica Italiana
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Editorial Board Ciro Ciliberto (Editor in Chief) Dipartimento di Matematica Universita` di Roma Tor Vergata Via della Ricerca Scientifica Roma, Italy e-mail: [email protected].it
Franco Flandoli Dipartimento di Matematica Applicata Universita` di Pisa Via Buonarroti c Pisa, Italy e-mail: fl[email protected]
Susanna Terracini (Co-editor in Chief) Universita` degli Studi di Torino Dipartimento di Matematica “Giuseppe Peano” Via Carlo Alberto Torino, Italy e-mail: [email protected]
Angus MacIntyre Queen Mary University of London School of Mathematical Sciences Mile End Road London E NS, United Kingdom e-mail: [email protected]
Adolfo Ballester-Bollinches ` Department d’Algebra Facultat de Matem`atiques Universitat de Vale` ncia Dr. Moliner, Burjassot (Vale` ncia), Spain e-mail: [email protected] Annalisa Buffa IMATI – C.N.R. Pavia Via Ferrata Pavia, Italy e-mail: [email protected] Lucia Caporaso Dipartimento di Matematica Universita` Roma Tre Largo San Leonardo Murialdo I- Roma, Italy e-mail: [email protected].it Fabrizio Catanese Mathematisches Institut Universita¨ tstraße Bayreuth, Germany e-mail: [email protected] Corrado De Concini Dipartimento di Matematica Universita` di Roma “La Sapienza” Piazzale Aldo Moro Roma, Italy e-mail: [email protected].it Camillo De Lellis Institut fur ¨ Mathematik Universita¨ t Zurich ¨ Winterthurerstrasse CH- Zurich, ¨ Switzerland e-mail: [email protected]
Giuseppe Mingione Dipartimento di Matematica e Informatica Universita` degli Studi di Parma Parco Area delle Scienze, /a (Campus) Parma, Italy e-mail: [email protected] Mario Pulvirenti Dipartimento di Matematica, Universita` di Roma “La Sapienza” P.le A. Moro Roma, Italy e-mail: [email protected].it Fulvio Ricci Scuola Normale Superiore di Pisa Piazza dei Cavalieri Pisa, Italy e-mail: [email protected] Valentino Tosatti Northwestern University Department of Mathematics Sheridan Road Evanston, IL , USA e-mail: [email protected] Corinna Ulcigrai Forschungsinstitut fur ¨ Mathematik HG G . R¨amistrasse Zurich, ¨ Switzerland e-mail: [email protected]
The Editorial Policy can be found at the back of the volume.
Lisa Beck
Elliptic Regularity Theory A First Course
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Lisa Beck Institut f¨ ur Mathematik Universit¨at Augsburg Augsburg, Germany
ISSN 1862-9113 ISSN 1862-9121 (electronic) Lecture Notes of the Unione Matematica Italiana ISBN 978-3-319-27484-3 ISBN 978-3-319-27485-0 (eBook) DOI 10.1007/978-3-319-27485-0 Library of Congress Control Number: 2015958734 Mathematics Subject Classification (2010): 35J47, 35B65, 49N60 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2016 Th
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