Mathematics 282 . Fall 2006 . Elliptic Partial Differential Equations

We fix once and for all a positive integer n. Unless we say otherwise, Ω will be an open subset of R. We let N; P; Z; Q; R; C be the set of nonnegative integers; the set of positive integers; the ring of integers; the field of rational numbers; the field of real numbers; and the field of complex numbers, respectively. Whenever a ∈ R and 0 < r <∞ we let U(a, r) = {x ∈ R : |x− a| < r} and B(a, r) = {x ∈ R : |x− a| ≤ r}.