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Nichtlineare Funktionalanalysis: Eine Einführung by Michael Růzička

Nichtlineare Funktionalanalysis: Eine Einführung

by Michael Růzička
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Book cover type: Paperback
  • ISBN13: 9783662621905
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer Spektrum
  • Publisher Imprint: Springer Spektrum
  • Publication Date:
  • Pages: 227
  • Original Price: EUR 42.05
  • Language: German
  • Edition: 2., Uberarb. Au
  • Item Weight: 341 grams
  • BISAC Subject(s): Functional Analysis

Dieses Lehrbuch enthält eine Einführung in die nichtlineare Funktionalanalysis. Die Themenauswahl vermittelt grundlegende Methoden und Techniken, die bei der Untersuchung von nichtlinearen elliptischen und parabolischen partiellen Differentialgleichungen Anwendung finden. Es geht insbesondere auf Fixpunktsätze, Differentiation und Integration in Banachräumen, die Theorie monotoner Operatoren und den Abbildungsgrad ein. Der Darstellung des Stoffes liegt die gegenseitige Beeinflussung von Theorie und Anwendungen zugrunde.

Kurze Einführungen am Kapitelanfang, illustrative Beispiele sowie die detaillierte Herleitung von Ergebnissen erleichtern das Verständnis. Eine Kurzzusammenfassung von wichtigen Resultaten aus der linearen Funktionalanalysis ist im Anhang zu finden und vervollständigt den Inhalt.

Das Buch richtet sich an Studierende mit abgeschlossener Grundausbildung in Analysis, linearer Algebra und linearer Funktionalanalysis und umfasst den Lehrstoff für eine vierstündige einsemestrige Vorlesung.

Für die 2. Auflage wurde insbesondere das Hauptkapitel zu monotonen Operatoren wesentlich überarbeitet. Es beinhaltet nun eine moderne Darstellung von Evolutionsproblemen mithilfe Bochner-pseudomonotoner Operatoren sowie eine in sich geschlossene Darstellung maximal monotoner Operatoren.

Prof. Dr. Michael Růzička forscht und lehrt an der Albert-Ludwigs-Universität Freiburg. Sein Arbeitsgebiet ist die theoretische und numerische Analysis nichtlinearer partieller Differentialgleichungen, insbesondere aus der Strömungsmechanik.

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