On a Priori Estimates and Fredholm Property of Differential Operators in Anisotropic Spaces

On a Priori Estimates and Fredholm Property of Differential Operators in Anisotropic Spaces

The paper is devoted to special a priori estimates and Fredholm property of differential operators acting in anisotropic Sobolev spaces in ℝ n . Necessary conditions for a priori estimates in terms of the symbol of an operator are obtained. Under appropriate conditions imposed on the coefficients, a...

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Veröffentlicht in:Journal of contemporary mathematical analysis 2018-03, Vol.53 (2), p.61-70
Hauptverfasser: Darbinyan, A. A., Tumanyan, A. G.
Format: Artikel
Sprache:eng
Schlagworte:
Differential equations
Estimates
Functional Analysis
Linear equations
Mathematics
Mathematics and Statistics
Operators
Sobolev space
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Beschreibung
Zusammenfassung:The paper is devoted to special a priori estimates and Fredholm property of differential operators acting in anisotropic Sobolev spaces in ℝ n . Necessary conditions for a priori estimates in terms of the symbol of an operator are obtained. Under appropriate conditions imposed on the coefficients, a priori estimates are obtained in the corresponding weighted spaces.
ISSN:1068-3623
1934-9416
DOI:10.3103/S1068362318020012