TY - JOUR
T1 - Multi-valued, singular stochastic evolution inclusions
AU - Gess, Benjamin
AU - Tölle, Jonas M.
PY - 2014
Y1 - 2014
N2 - We provide an abstract variational existence and uniqueness result for multi-valued, monotone, non-coercive stochastic evolution inclusions in Hilbert spaces with general additive and Wiener multiplicative noise. As examples we discuss certain singular diffusion equations such as the stochastic 1-Laplacian evolution (total variation flow) in all space dimensions and the stochastic singular fast-diffusion equation. In case of additive Wiener noise we prove the existence of a unique weak*-mean ergodic invariant measure.
AB - We provide an abstract variational existence and uniqueness result for multi-valued, monotone, non-coercive stochastic evolution inclusions in Hilbert spaces with general additive and Wiener multiplicative noise. As examples we discuss certain singular diffusion equations such as the stochastic 1-Laplacian evolution (total variation flow) in all space dimensions and the stochastic singular fast-diffusion equation. In case of additive Wiener noise we prove the existence of a unique weak*-mean ergodic invariant measure.
KW - Ergodic semigroup
KW - Logarithmic diffusion
KW - p-Laplacian equation
KW - Singular stochastic evolution equation
UR - http://www.scopus.com/inward/record.url?scp=84900014724&partnerID=8YFLogxK
U2 - 10.1016/j.matpur.2013.10.004
DO - 10.1016/j.matpur.2013.10.004
M3 - Article
AN - SCOPUS:84900014724
SN - 0021-7824
VL - 101
SP - 789
EP - 827
JO - JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
JF - JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
IS - 6
ER -