For SPDEs with symmetric stable operators of order alpha in bounded C^{1,sigma} domains, the paper proves existence, uniqueness, and maximal weighted Sobolev regularity under generalized Gaussian noise.
Sobolev regularity theory for stochastic reaction-diffusion-advection equations with spatially homogeneous colored noises and infinitesimal generators of subordinate Brownian motions
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abstract
This article investigates the existence, uniqueness, and regularity of solutions to nonlinear stochastic reaction-diffusion-advection equations (SRDAEs) with spatially homogeneous colored noises and infinitesimal generators of subordinate Brownian motions in mixed norm $L_q(L_p)$-spaces. We introduce a new condition (strongly reinforced Dalang's condition) on colored noise, which facilitates a deeper understanding of the complicated relation between nonlinearities and stochastic forces. Additionally, we establish the space-time H\"older type regularity of solutions.
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The Dirichlet problem for stochastic partial differential equations with nonlocal operators in $C^{1,\sigma}$ open sets
For SPDEs with symmetric stable operators of order alpha in bounded C^{1,sigma} domains, the paper proves existence, uniqueness, and maximal weighted Sobolev regularity under generalized Gaussian noise.