On the Variational Inequalities for Certain Convex Function Classes

Hi Jun Choe, Yong Sun Shim

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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
Volume115
Issue number2
DOIs
Publication statusPublished - 1995 Jan 20

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Variational Inequalities
Convex function
Regularity
Viscosity
Obstacle Problem
Hamilton-Jacobi Equation
Viscosity Solutions
Weak Solution
Interior
Imply
Closed
Class

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

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On the Variational Inequalities for Certain Convex Function Classes. / Choe, Hi Jun; Shim, Yong Sun.

In: Journal of Differential Equations, Vol. 115, No. 2, 20.01.1995, p. 325-349.

Research output: Contribution to journalArticle

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