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

  • Gadoev Makhmadrakhim G., gadoev@rambler.ru North-Eastern Federal University, Mirny Polytechnic Institute (branch), 5/1 Tikhonov Street, Mirny 678170, Yakutia, Russia
  • Iskhokov Faridun S., fariduniskhokov@mail.ru Academy of Sciences of the Republic of Tajikistan, A. Dzhuraev Mathematical Institute, 299/4 Aini Street, Dushanbe 734063, Tajikistan
Keywords: partial differential operator, non-power degeneration, right-hand regularizing operator, inverse operator, partition of unity

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.

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How to Cite
Gadoev, M. and Iskhokov, F. (2016) “On invertibility of a class of degenerate differential operators in the Lebesgue space”, Mathematical notes of NEFU, 23(3), pp. 3-26. Available at: http://mzsvfu.ru/index.php/mz/article/view/on-invertibility-of-a-class-of-degenerate-differential-operators-in-the-lebesgue-space (Accessed: 22September2020).
Section
Mathematics