et
be an open bounded subset of
.
The
are
functions
.
The
is a linear differential
operator


(Operator L)

Problem
(Elliptic Dirichlet
problem).
Let us multiply the equations of the problem
(
Elliptic Dirichlet problem
) with a
function
and integrate with respect to
over
.
After integration by parts we
obtain
Definition
(Weak solution of
elliptic Dirichlet problem). The function
is a "weak solution" of the problem
(
Elliptic Dirichlet problem
) if it
satisfies
