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One-sided problems for elliptic operators with convex constraints on the gradient of the solution. I. (English. Russian original) Zbl 0587.35040
Sib. Math. J. 26, 414-424 (1985); translation from Sib. Mat. Zh. 26, No. 3(151), 134-146 (1985).
The author coniders a one-sided problem for a second order elliptic operator in a bounded domain \(\Omega\) with a \(C^ 2\)-boundary, proving the existence of a solution of class \(\cap_{1<p<\infty}W^ 2_{p,loc} (\Omega)\cap C^{0,1}({\bar \Omega})\) under certain conditions on the coefficients of the operator and on the closed convex sets associated with the problem.
Reviewer: C.Constanda

MSC:
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
35D05 Existence of generalized solutions of PDE (MSC2000)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35J15 Second-order elliptic equations
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