Last Updated：2022/12/24
The first notion of a Laplace operator for functionals on a Hilbert space was introduced by Levy in [l], and the idea was developed further in [2]. Levy's results depended on the posthumous work of Gateaux [3] in which the Dirichlet problem in Hilbert space was considered (without any concise definition of the Laplace operator).
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The
first
notion
of
a
Laplace
operator
for
functionals
on
a
Hilbert
space
was
introduced
by
Levy
in
[l],
and
the
idea
was
developed
further
in
[2].
Levy's
results
depended
on
the
posthumous
work
of
Gateaux
[3]
in
which
the
Dirichlet
problem
in
Hilbert
space
was
considered
(without
any
concise
definition
of
the
Laplace
operator).
