Some Properties of Traces for Stochastic and Deterministic Parabolic Weighted Sobolev Spaces

The results presented provide information on the behavior near x1=0 for fixed t>0 in the sense of Lp-spaces with weights for functions u(t)=u(t, x1, x′) (x1⩾0, x′∈Rd−1, t⩾0) satisfying stochastic partial differential equations of type du(t)=(Δu(t)+f(t)) dt+gk(t) dwkt with zero boundary condition on x1=0.