Competing Operators and Their Applications to Boundary Value Problems
-
- Taschenbuch ausgewählt
- eBook
-
Sprache:Englisch
45,99 €
inkl. gesetzl. MwSt.,
Beschreibung
Produktdetails
Einband
Taschenbuch
Erscheinungsdatum
23.02.2026
Abbildungen
X, 1 illus., schwarz-weiss Illustrationen
Verlag
SpringerSeitenzahl
102
Maße (L/B/H)
23,5/15,5/0,7 cm
Gewicht
184 g
Sprache
Englisch
ISBN
978-3-032-15444-6
This book addresses problems driven by differential operators that lack monotonicity. The authors’ methods rely on coercivity and continuity, allowing for the construction of an approximative scheme whose convergence is induced by coercivity.
This observation leads to a new type of solution, which is precisely a limit of finite-dimensional approximation schemes and leads to the weak solution, provided that the operator driving the equation is at least pseudomonotone. This new type of solution is called a generalized solution. To systematically treat its existence, the authors introduce an abstract existence tool that serves as a counterpart to the Browder-Minty Theorem in the non-variational case and the Weierstrass-Tonelli Theorem if the problem is potential. Thus, the authors utilize many already developed techniques, suitably modified due to the absence of the monotonicity assumption.
The authors obtain three abstract results, also in the non-smooth case, which they apply to nonlinear boundary value problems. In their applications, they also deal with problems depending on an unbounded weight, which forces them to implement a suitable truncation technique.
The book includes an extended chapter covering analysis on abstract tools from the theory of monotone operators and minimization techniques, supplied with proofs and comments that allow for a better understanding of the authors’ approach towards generalized solutions. It includes necessary background on Sobolev spaces, introduces the non-variational generalized solution, and investigates the existence of solutions for variational problems and inclusions.
Noch keine Bewertungen vorhanden
Verfassen Sie die erste Bewertung zu diesem Artikel
Helfen Sie anderen Kundinnen und Kunden durch Ihre Meinung.
Kurze Frage zu unserer Seite
Vielen Dank für Ihr Feedback
Wir nutzen Ihr Feedback, um unsere Produktseiten zu verbessern. Bitte haben Sie Verständnis, dass wir Ihnen keine Rückmeldung geben können. Falls Sie Kontakt mit uns aufnehmen möchten, können Sie sich aber gerne an unseren Kund*innenservice wenden.
zum Kundenservice