A Priori Estimate of Solutions of One Boundary-Value Problem in a Strip for a Higher-Order Degenerate Elliptic Equation

In this paper, we prove coercive a priori estimates of solutions of a Dirichlet-type boundary-value problem in a strip for a certain higher-order degenerate elliptic equation containing weighted derivatives of a special form up to the order 2 m and ordinary partial derivatives up to the order 2 k− 1...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 268; no. 1; pp. 114 - 123
Main Authors Pankov, V. V., Baev, A. D., Kharchenko, V. D., Babaitsev, A. A.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.11.2022
Springer
Springer Nature B.V
Subjects
Boundary value problems
Coercivity
Dirichlet problem
Mathematical analysis
Mathematics
Mathematics and Statistics
Strip
35S11
Sobolev weight space
a priori estimate
35S05
degenerate elliptic equation
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Summary:In this paper, we prove coercive a priori estimates of solutions of a Dirichlet-type boundary-value problem in a strip for a certain higher-order degenerate elliptic equation containing weighted derivatives of a special form up to the order 2 m and ordinary partial derivatives up to the order 2 k− 1 under the condition 2 m > 2 k − 1. At the boundary of the strip, Dirichlet-type conditions are imposed. A coercive a priori estimate for solutions of the problem considered in special weighted Sobolev-type spaces is obtained.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-06183-2