scholarly journals Function Spaces with a Random Variable Exponent

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Boping Tian ◽  
Yongqiang Fu ◽  
Bochi Xu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Variable Exponent ◽  
Random Variable ◽  
Function Spaces ◽  
Partial Differential

The spaces with a random variable exponent and are introduced. After discussing the properties of the spaces and , we give an application of these spaces to the stochastic partial differential equations with random variable growth.

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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