Functional Analysis, Sobolev Spaces and Partial ...

UniversitextFor other titles in this series, go CHaim BrezisFunctional analysis , Sobolev Spaces and Partial Differential EquationsHaim BrezisDistinguished ProfessorDepartment of MathematicsRutgers UniversityPiscataway, NJ m rite, Universit Pierre et Marie Curie (Paris 6) andVisiting Distinguished Professor at the TechnionEditorial board:Sheldon Axler, San Francisco State UniversityVincenzo Capasso, Universit degli Studi di MilanoCarles Casacuberta, Universitat de BarcelonaAngus MacIntyre, Queen Mary, University of LondonKenneth Ribet, University of California, BerkeleyClaude Sabbah, CNRS, cole PolytechniqueEndre S li, University of OxfordWojbor Woyczy ski, Case Western Reserve UniversityISBN 978-0-387-70913-0 e-ISBN 978-0-387-70914-7 DOI New York Dordrecht Heidelberg LondonLibrary of Congress Control Number: 2010938382 Mathematics Subject Classification (2010): 35 Rxx, 46 Sxx, 47 Sxx Spri

We recall that a functional is a function defined on E, or on some subspace of E, with values in R. The main result of this section concerns the extension of a linear functional defined on a linear subspace of E by a linear functional defined on all of E. Theorem 1.1 (Helly, Hahn–Banach analytic form). Let p: E → R be a function satisfying1

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  Analysis, Functional, Space, Functional analysis, Sobolev, Sobolev spaces and

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