Title
Monotone Potentialoperatoren In Theorie Und Anwendung (Hochschultext) (German Edition),Used
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In der angewandten Funktionalanalysis sind in den letzten Jahrzehnten verschie dene relativ abgeschlossene Theorien zur Losung nichtlinearer Probleme entstanden, unter denen die Methode der monotonen Operatoren und die Variationsmethoden mit Potentialoperatoren einen hervorragenden Platz einnehmen. Die 'Monotonietheorie' entstand vornehmlich im Rahmen der funktionalanaly tischen Behandlungsweise von Randwertproblemen fur elliptische Differentialglei chungen. In engem Zusammenhang mit diesen Randwertproblemen entwickelte sich auch die Theorie der Potentialoperatoren. Potentialoperatoren sind Gradienten differenzierbarer Funktionale; sie treten daher zwangslaufig bei der Anwendung von Variationsmethoden auf. Mit Hille monotoner Potentialoperatoren kann man elliptische Differentialgleichun gen modellieren und lOsen, die aus einem Variationsprinzip hergeleitet werden konnen. Ein ausgereiftes Konzept dieser Methode und seine Realisierung, die von der Model lierung bis zur konstruktiven Losung reichte, fand sich bereits in dem 1950 erschienenen Buch von S. G. MICHLIN [65], dem weitere Bucher dieses Autors folgten [68], [69]. 1m Jahre 1956 erschienen zwei Bucher uber nichtlineare Operatoren in der Funktio nalanalysis von M. A. KRASNOSEL'SKIJ [38] und M. M. V AJNBERG [87] mit Anwen dungen in der Theorie der Integralgleichungen. In dem Buch von M. M. V AJNBERG wurden gelegentlich monotone Potentialoperatoren benutzt. Der Monotoniebegriff selbst wurde jedoch spater gepragt, siehe R. I. KAcuROVSKIJ [31], G. J. MINTY [70].
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