# REGULARITY OF NONLINEAR VECTOR VALUED VARIATIONAL INEQUALITIES

• Kim, Do-Wan (Department of Mathematics Sunmoon University)
• Published : 2000.07.01
• 45 3

#### Abstract

We consider regularity questions arising in the degenerate elliptic vector valued variational inequalities -div(｜▽u｜p-2∇u)$\geq$b(x, u, ∇u) with p$\in$(1, $\infty$). It is a generalization of the scalar valued inequalities, i.e., the obstacle problem. We obtain the C1,$\alpha$loc regularity for the solution u under a controllable growth condition of b(x, u, ∇u).

#### Keywords

vector valued variational inequalities;regularity;maximum principle

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