Second Order Partial Differential Equation...

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Sprache: Englisch

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Beschreibung

Second order linear parabolic and elliptic equations arise frequently in mathematics and other disciplines. For example parabolic equations are to be found in statistical mechanics and solid state theory, their infinite dimensional counterpart are important in fluid mechanics, mathematical finance and population biology, whereas nonlinear parabolic equations arise in control theory. Here the authors present a state of the art treatment of the the subject from a new perspective. The main tools used are probability measures in Hilbert and Banach spaces and stochastic evolution equations. There is then a discussion of how the results in the book can be applied to control theory. This area is developing very rapidly and there are numerous notes and references that point the reader to more specialised results not covered in the book. Coverage of some essential background material will help make the book self-contained and increase its appeal to those entering the subject.

Inhaltsverzeichnis

Part I. Theory in the Space of Continuous Functions: 1. Gaussian measures; 2. Spaces of continuous functions; 3. Heat equation; 4. Poisson's equation; 5. Elliptic equations with variable coefficients; 6. Ornstein-Uhlenbeck equations; 7. General parabolic equations; 8. Parabolic equations in open sets; Part II. Theory in Sobolev Spaces with a Gaussian Measure: 9. L2 and Sobolev spaces; 10. Ornstein-Uhlenbeck semigroups on Lp(H, mu); 11. Perturbations of Ornstein-Uhlenbeck semigroups; 12. Gradient systems; Part II. Applications to Control Theory: 13. Second order Hamilton-Jacobi equations; 14. Hamilton-Jacobi inclusions.

Erscheinungsjahr:	2004
Fachbereich:	Analysis
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	Kartoniert / Broschiert
ISBN-13:	9780521777292
ISBN-10:	0521777291
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Da Prato, Giuseppe Zabczyk, Jerzy Prato, Giuseppe Da
Hersteller:	Cambridge University Press
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	229 x 152 x 23 mm
Von/Mit:	Giuseppe Da Prato (u. a.)
Erscheinungsdatum:	28.01.2004
Gewicht:	0,641 kg

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