Abstract
In the half-space, we obtain a coercive a priori estimation of solutions to the boundary value problem for a degenerate pseudodifferential equation. The left-hand side of the equation is the sum of a pseudo-differential operator with degeneracy, constructed by a special integral transform, and the differentiation operator. The a priori estimation is obtained in special weight spaces of Sobolev type, the norms in which are constructed with the use of a special integral transformation.
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Funding
The work is fulfilled under financial support of the Russian Science Foundation (project no. 19–11–00197).
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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 5, pp. 6–10.
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Baev, A.D., Chechin, D.A., Shabrov, S.A. et al. A Priori Estimation of Solutions of a Boundary Problem for a Pseudodifferential Equation with Degeneration. Russ Math. 65, 1–3 (2021). https://doi.org/10.3103/S1066369X21050017
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DOI: https://doi.org/10.3103/S1066369X21050017