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Equivalence of variational inequalities with Wiener-Hopf equations. (English) Zbl 0881.35049
The author compares a variational inequality (Au,v-u)(f,v-u) for all vK and a generalized Wiener-Hopf equation (AP+Q)v=f, where A:D(A)H is an arbitrary operator, H is a Hilbert space, K its closed convex subset, P the projection operator from H into K, Q=I-P. The main results are as follows: The variational inequality has a solution u if and only if the Wiener-Hopf equation has a solution v, v=u+f-Au, u=Pv. If a solution u is unique for each f, then u=P(AP+Q) -1 f.

MSC:
35J85Unilateral problems; variational inequalities (elliptic type) (MSC2000)
35A15Variational methods (PDE)
35K85Linear parabolic unilateral problems; linear parabolic variational inequalities