# The Obstacle Problems: A Regularity Theory

• M. Chipot
Chapter
Part of the Applied Mathematical Sciences book series (AMS, volume 52)

## Abstract

Throughout this chapter, Ω will be a bounded domain of ℝn with boundary Γ and aij 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)