Indexing metadata

Is the stochastic parabolicity condition dependent on $p$ and $q$?


 
Dublin Core PKP Metadata Items Metadata for this Document
 
1. Title Title of document Is the stochastic parabolicity condition dependent on $p$ and $q$?
 
2. Creator Author's name, affiliation, country Zdzislaw Brzezniak; University of York; United Kingdom
 
2. Creator Author's name, affiliation, country Mark Veraar; Delft University of Technology; Netherlands
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) stochastic parabolicity condition; parabolic stochastic evolution; multiplicative noise; gradient noise; blow-up; strong solution; mild solution; maximal regularity; stochastic partial differential equation
 
3. Subject Subject classification 60H15; 35R60
 
4. Description Abstract

In this paper we study well-posedness of a second order SPDE with multiplicative noise on the torus $\mathbb{T} = [0,2\pi]$. The equation is considered in $L^p((0,T)\times\Omega;L^q(\mathbb{T}))$ for $p,q\in (1, \infty)$. It is well-known that if the noise is of gradient type, one needs a stochastic parabolicity condition on the coefficients for well-posedness with $p=q=2$. In this paper we investigate whether the well-posedness depends on $p$ and $q$. It turns out that this condition does depend on $p$, but not on $q$. Moreover, we show that if $1<p<2$ the classical stochastic parabolicity condition can be weakened.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2012-07-22
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2186
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-2186
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
15. Rights Copyright and permissions The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.

Summary of the Creative Commons Attribution License

You are free
  • to copy, distribute, display, and perform the work
  • to make derivative works
  • to make commercial use of the work
under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.