We study the Robin boundary-value problem for bounded domains with isolated singularities. Because trace spaces of space
W
2
1
(
D
)
W_{2}^{1}(D)
on boundaries of such domains are weighted Sobolev spaces
L
2
,
ξ
(
∂
D
)
L^{2,\xi }(\partial D)
, existence and uniqueness of corresponding Robin boundary-value problems depends on properties of embedding operators
I
1
:
W
2
1
(
D
)
→
L
2
(
D
)
I_{1}:W_{2}^{1}(D)\rightarrow L^{2}(D)
and
I
2
:
W
2
1
(
D
)
→
L
2
,
ξ
(
∂
D
)
I_{2}:W_{2}^{1}(D)\rightarrow L^{2,\xi }(\partial D)
i.e. on types of singularities. We obtain an exact description of weights
ξ
\xi
for bounded domains with ‘outside peaks’ on its boundaries. This result allows us to formulate correctly the corresponding Robin boundary-value problems for elliptic operators. Using compactness of embedding operators
I
1
,
I
2
I_{1},I_{2}
, we prove also that these Robin boundary-value problems with the spectral parameter are of Fredholm type.