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Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise


 
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1. Title Title of document Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise
 
2. Creator Author's name, affiliation, country Raphael Kruse; Bielefeld University; Germany
 
2. Creator Author's name, affiliation, country Stig Larsson; Chalmers University of Technology and University of Gothenburg; Sweden
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) SPDE; Hölder continuity; temporal and spatial regularity; multiplicative noise; Lipschitz nonlinearities; linear growth bound
 
3. Subject Subject classification 35B65; 35R60; 60H15
 
4. Description Abstract

This paper deals with the spatial and temporal regularity of the unique Hilbert space valued mild solution to a semilinear stochastic parabolic partial differential equation with nonlinear terms that satisfy global Lipschitz conditions and certain linear growth bounds. It is shown that the mild solution has the same optimal regularity properties as the stochastic convolution. The proof is elementary and makes use of existing results on the regularity of the solution, in particular, the Hölder continuity with a non-optimal exponent.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) First author: German Research Foundation (DFG) through CRC 701 and IGK 1132. Second author: Swedish Research Council (VR) and Swedish Foundation for Strategic Research (SSF) through GMMC.
 
7. Date (YYYY-MM-DD) 2012-08-18
 
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/2240
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-2240
 
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.)
 
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