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.
Aikawa, Quasiadditivity of Riesz capacity, Math
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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.