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

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.

### References

Received

14-01-2016

How to Cite

*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).

Issue

Section

Mathematics

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