The Obstacle Problems: A Regularity Theory

Abstract

Throughout this chapter, Ω will be a bounded domain of ℝⁿ with boundary Γ and a_ij functions in L^∞ (Ω) which satisfy the ellipticity assumption

$${a_{ij}}(x){\xi _i}{\xi _j}\upsilon |\xi {|^2}\forall x \in \Omega ,\forall \xi \in {R^n}$$

(3.1)

We will denote by A the operator

$${\text{A}} = \frac{\partial }{{\partial {x_i}}}({a_{ij}}(x)\frac{\partial }{{\partial {x_j}}}).$$

(3.2)