On the Necessary Conditions of Optimal Controls for Stochastic Partial Differential Equations

1993 ◽  
Vol 31 (6) ◽  
pp. 1462-1478 ◽  
Author(s):  
Xun Yu Zhou
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Necessary Conditions ◽  
Optimal Controls ◽  
Partial Differential

scholarly journals Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients

2021 ◽  
Author(s):  
Shohei Nakajima
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Stochastic Partial Differential Equations ◽  
Fractional Laplacian ◽  
Existence Of Solutions ◽  
Partial Differential ◽  
Continuity Theorem ◽  
Existence Of Weak Solutions ◽  
One Dimensional

AbstractWe prove existence of solutions and its properties for a one-dimensional stochastic partial differential equations with fractional Laplacian and non-Lipschitz coefficients. The method of proof is eatablished by Kolmogorov’s continuity theorem and tightness arguments.

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