 
Summary: Mathematics 282. Fall 2006. Elliptic Partial
Differential Equations.
William K. Allard
October 10, 2006
Contents
1 Some basic notations and conventions.
We fix once and for all a positive integer n. Unless we say otherwise, will be
an open subset of Rn
.
We let
N; P; Z; Q; R; C
be the set of nonnegative integers; the set of positive integers; the ring of in
tegers; the field of rational numbers; the field of real numbers; and the field of
complex numbers, respectively.
Whenever a Rn
and 0 < r < we let
U(a, r) = {x Rn
: x  a < r} and B(a, r) = {x Rn
: x  a r}.
We let
