Besov Regularity of Stochastic Partial Differential Equations on Bounded Lipschitz Domains
By (author) Petru Cioica
Paperback (Published)
(March 2015)
ISBN: 9783832539207
5.71 x 8.27 inches
Price: $53.00
In stock
Stochastic partial differential equations (SPDEs, for short) are the mathematical models of choice for space time evolutions corrupted by noise. Although in many settings it is known that the resulting SPDEs have a unique solution, in general, this solution is not given explicitly. Thus, in order to make those mathematical models ready to use for real life applications, appropriate numerical algorithms are needed. To increase efficiency, it would be tempting to design suitable adaptive schemes based, e.g., on wavelets. However, it is not a priori clear whether such adaptive strategies can outperform well-established uniform alternatives. Their theoretical justification requires a rigorous regularity analysis in so-called non-linear approximation scales of Besov spaces. In this thesis the regularity of (semi-)linear second order SPDEs of Ito type on general bounded Lipschitz domains is analysed. The non-linear approximation scales of Besov spaces are used to measure the regularity with respect to the space variable, the time regularity being measured first in terms of integrability and afterwards in terms of Hlder norms. In particular, it is shown that in specific situations the spatial Besov regularity of the solution in the non-linear approximation scales is generically higher than its corresponding classical Sobolev regularity. This indicates that it is worth developing spatially adaptive wavelet methods for solving SPDEs instead of using uniform alternatives.
- By (author) Petru Cioica
Similar Books
![Book cover: Transitive Media [Philosophy]](https://isd.stisonbooks.com/images/books/native/9781804132340.jpg?asset_id=66970)
Care in an Era of New Technologies and Artificial Intelligence
Relationships in a Connected World
Volume 14
Buchblogs zwischen Passion und Profession
Zur Diskursivierung digitaler literaturbezogener Anschlusskommunikation als Arbeit
Volume 5
Proceedings of the 7th Symposium of the Hellenic Society for Archaeometry
Archaeology Archaeometry: 30 Years Later
Die Einfuhrung ins richtige Handeln in der Arithmetik (Madhal ar-rasad ila ‘ilm al-‘adad) von al-Qalasadi (st. 1486)
Bearbeitung und Einordnung in die magribinische Mathematikgeschichte
Volume 19
I disegni e i discorsi di Giovanni Antonio Nigrone vol. I
fontanaro e ingegniero de acqua (1585-1609 ca.)
Volume 481
I disegni e i discorsi di Giovanni Antonio Nigrone vol. II
Fontanaro e ingegniero de acqua (1585-1609 ca.)
Volume 497
Performance Management in Humanitarian Logistics
Development of a Process-driven and IT-supported Performance Measurement System
Volume 66
Supporting Operational and Real-time Planning Tasks of Road Freight Transport with Machine Learning
Guiding the Implementation of Machine Learning Algorithms
Volume 69
