Mathematics

On invertibility of a class of degenerate differential operators in the Lebesgue space

M. G. Gadoev^a, F. S. Iskhokov<sup>b

a</sup> North-Eastern Federal University, Mirny Polytechnic Institute (branch), 5/1 Tikhonov Street, Mirny 678170, Yakutia, Russia
^b Academy of Sciences of the Republic of Tajikistan, A. Dzhuraev Mathematical Institute, 299/4 Aini Street, Dushanbe 734063, Tajikistan

Abstract: We construct the right-hand regularizing operator for a class of partial differential operators in non-divergent form in an arbitrary (bounded or unbounded) domain in the $n$-dimensional Euclidian space with non-power degeneracy on the boundary. On its base we prove the existence of the inverse operator in the Lebesgue space.

Keywords: partial differential operator, non-power degeneration, right-hand regularizing operator, inverse operator, partition of unity.

UDC: 517.957

Received: 14.01.2016

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