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| Quasi-sure Flows Associated with Vector Fields ofLow Regularity? |
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Citation： |
Siyan XU,Hua ZHANG.Quasi-sure Flows Associated with Vector Fields ofLow Regularity?[J].Chinese Annals of Mathematics B,2014,35(1):51~68 |
| Page view： 1620
Net amount： 1089 |
Authors： |
Siyan XU; Hua ZHANG; |
Foundation： |
National Natural Science Foundation of China (Nos. 11171358, 11026202,11101441), the Doctor Fund of Ministry of Education (Nos. 20100171110038, 20100171120041) and theNatural Science Foundation of Guangdong Province (No. S2012040007458). |
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| Abstract： |
The authors construct a solution Ut(x) associated with a vector field on the
Wiener space for all initial values except in a 1-slim set and obtain the 1-quasi-sure flow
property where the vector field is a sum of a skew-adjoint operator not necessarily bounded
and a nonlinear part with low regularity, namely one-fold differentiability. Besides, the
equivalence of capacities under the transformations of the Wiener space induced by the
solutions is obtained. |
Keywords： |
Quasi-sure flows, Abstract Wiener space, Low regularity |
Classification： |
60H07, 60H20, 60H30 |
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