Abstract
Let be a smooth unbounded domain in
conical at infinity,
We consider general transmission problems defined by a differential equation
1 and transmission conditions on the boundary
2 where the coefficients
are discontinuous on
functions, such that
the space of infinitely differentiable functions in
bounded with all derivatives,
is a jump of the function
on
We give a criterion for the operator
of the transmission problem (1) and (2) to be Fredholm. We also extend this result to more general quasi-conical at infinity domains. This criterion is applied to the anisotropic acoustic problem
3 where
is a uniformly positive definite matrix on
with discontinuous on
entries
such that
,
is discontinuous on
function such that
is a conormal derivative. We prove that if the acoustic medium is absorbed at infinity the problem (3) has an unique solution
for every
Acknowledgements
The author is grateful to the National System of Researchers of Mexico (SNI) for a support of his scientific activity.
Notes
The paper is partially supported by the CONACYT project 000000000179872.