On the Variational Inequalities for Certain Convex Function Classes

Hi Jun Choe, Yong Sun Shim

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The existence and the C1,α regularity of the weak solution to the variation inequality -(ai(x, u, ∇u))x i - (gi(x, u))x i + b(x, u, ∇u) ≥ 0 with respect to a closed convex function class is proved. For the regularity, we use the fact that the regularity for the viscosity solutions to the Hamilton-Jacobi equations implies the C1, α interior regularity of the solution to the bilateral obstacle problem which in turn gives that of the solution to the variational inequality.

Original languageEnglish
Pages (from-to)325-349
Number of pages25
JournalJournal of Differential Equations
Issue number2
Publication statusPublished - 1995 Jan 20


All Science Journal Classification (ASJC) codes

  • Analysis

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