Geodesic
A priori estimation of solutions of a boundary problem for a pseudodifferential equation with degeneration
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2021), pp. 6-10

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In this paper, we obtain a coercive a priori estimation of solutions to the boundary value problem in a half-space for a degenerate psedodifferential equation. The left part of the equation is the sum of the pseudo-differential operator with degeneracy, constructed by a special integral transformation, and the differentiation operator. A priori estimation is obtained in special weight spaces of the type of S. L. Sobolev spaces, the norms in which are constructed using a special integral transformation.
Mots-clés : a priori estimation
Keywords: degenerate equation, pseudo-differential operator with degeneration, S. L. Sobolev weight spaces. 
@article{IVM_2021_5_a1,
     author = {A. D. Baev and D. A. Chechin and S. A. Shabrov and N. I. Rabotinskaya and N. A. Babaitseva},
     title = {A priori estimation of solutions of a boundary problem for a pseudodifferential equation with degeneration},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {6--10},
     publisher = {mathdoc},
     number = {5},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_5_a1/}
}
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A. D. Baev; D. A. Chechin; S. A. Shabrov; N. I. Rabotinskaya; N. A. Babaitseva. A priori estimation of solutions of a boundary problem for a pseudodifferential equation with degeneration. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2021), pp. 6-10. http://geodesic.mathdoc.fr/item/IVM_2021_5_a1/