Abstract
AbstractWe consider m-th order linear, uniformly elliptic equations $$\mathcal {L}u=f$$
L
u
=
f
with non-smooth coefficients in Banach–Sobolev spaces $$W_{X_w}^m (\Omega )$$
W
X
w
m
(
Ω
)
generated by weighted Banach Function Spaces (BFS) $$X_w (\Omega )$$
X
w
(
Ω
)
on a bounded domain $$\Omega \subset {\mathbb R}^{n}$$
Ω
⊂
R
n
. Supposing boundedness of the Hardy–Littlewood Maximal operator and the Calderón–Zygmund singular integrals in $$X_w (\Omega )$$
X
w
(
Ω
)
we obtain solvability in the small in $$W_{X_w}^m (\Omega )$$
W
X
w
m
(
Ω
)
and establish interior Schauder type a priori estimates. These results will be used in order to obtain Fredholmness of the operator $$\mathcal {L}$$
L
in $$X_w (\Omega )$$
X
w
(
Ω
)
.
Funder
Università degli Studi di Salerno
Publisher
Springer Science and Business Media LLC
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