A Priori Estimation of Solutions of a BoundaryProblem for a Pseudodifferential Equation with Degeneration

A Priori Estimation of Solutions of a BoundaryProblem for a Pseudodifferential Equation with Degeneration

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 d...

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Veröffentlicht in:Russian mathematics 2021-01, Vol.65 (5), p.1-3
Hauptverfasser: Baev, A D, Chechin, D A, Shabrov, S A, Rabotinskaya, N I, Babaitseva, N A
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Boundary value problems
Coercivity
Degeneration
Differential equations
Half spaces
Integral transforms
Norms
Operators (mathematics)
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container_end_page 3
container_issue 5
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container_title Russian mathematics
container_volume 65
creator Baev, A D
Chechin, D A
Shabrov, S A
Rabotinskaya, N I
Babaitseva, N A
description 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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subjects Boundary value problems
Coercivity
Degeneration
Differential equations
Half spaces
Integral transforms
Norms
Operators (mathematics)
title A Priori Estimation of Solutions of a BoundaryProblem for a Pseudodifferential Equation with Degeneration
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