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.
Bibliographical noteFunding Information:
1The work was partially supported by NSF Grant DMS-9876586.
Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.
- Embedding theorems; Sobolev spaces with weights