Abstract
We consider general second-order linear elliptic partial differential equations having random coefficients and random data and fulfilling the homogeneous Dirichlet condition. We prove the existence and uniqueness of the weak solution in a certain tensor product space which is suitably completed to make it a Hilbert space. The factors of this space are a Sobolev space of functions depending on the space variable and a general Sobolev space of functions depending on the stochastic variable.
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