UCL  IRIS
Institutional Research Information Service
UCL Logo
Please report any queries concerning the funding data grouped in the sections named "Externally Awarded" or "Internally Disbursed" (shown on the profile page) to your Research Finance Administrator. Your can find your Research Finance Administrator at https://www.ucl.ac.uk/finance/research/rs-contacts.php by entering your department
Please report any queries concerning the student data shown on the profile page to:

Email: portico-services@ucl.ac.uk

Help Desk: http://www.ucl.ac.uk/ras/portico/helpdesk
Publication Detail
Refined existence and regularity results for a class of semilinear dissipative SPDEs
Abstract
© 2020 World Scientific Publishing Company. We prove the existence and uniqueness of solutions to a class of stochastic semilinear evolution equations with a monotone nonlinear drift term and multiplicative noise, considerably extending corresponding results obtained in previous work of ours. In particular, we assume the initial datum to be only measurable and we allow the diffusion coefficient to be locally Lipschitz-continuous. Moreover, we show, in a quantitative fashion, how the finiteness of the pth moment of solutions depends on the integrability of the initial datum, in the whole range p[0,∞[. Lipschitz continuity of the solution map in pth moment is established, under a Lipschitz continuity assumption on the diffusion coefficient, in the even larger range p [0,∞[. A key role is played by an Itô formula for the square of the norm in the variational setting for processes satisfying minimal integrability conditions, which yields pathwise continuity of solutions. Moreover, we show how the regularity of the initial datum and of the diffusion coefficient improves the regularity of the solution and, if applicable, of the invariant measures.
Publication data is maintained in RPS. Visit https://rps.ucl.ac.uk
 More search options
UCL Researchers
Author
Dept of Mathematics
University College London - Gower Street - London - WC1E 6BT Tel:+44 (0)20 7679 2000

© UCL 1999–2011

Search by