
17.4. Boundary Value Problems with Many Space Variables. Green’s Function 1219
with the nonhomogeneous initial condition of the special form
G = δ(x − y) at t = τ (17.4.1.7)
and the homogeneous boundary condition
Γ
x
[G] = 0 for x ∈ S. (17.4.1.8)
The vector y = {y
1
, . . . , y
n
} appears in problem (17.4.1.6)–(17.4.1.8) as an n-dimensional
free parameter (y ∈ V ), and δ(x − y) = δ(x
1
− y
1
) . . . δ(x
n
− y
n
) is the n-dimensional
Dirac delta function. The Green’s function G is independent of the functions Φ, f, and g
that characterize various inhomogeneities of the boundary value problem. In (17.4.1.5), the
integration is performed everywhere with respect to ...