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Elliptic Functional Differential Equations with Degenerations

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Abstract

This review is devoted to differential-difference equations with degeneration in a bounded domain \(Q\subset\mathbb{R}^{n}\) and applications (Kato conjecture, nonlocal boundary value problem). We consider differential-difference operators with degeneration of the second order and generalization to \(2m\)-order and the case where differential-difference operator contains several degenerate difference operators with degeneration. Generalized solutions of such equations may not belong even to the Sobolev space \(W^{1}_{2}(Q)\).

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Funding

The work is supported by the Ministry of Education and Science of Russian Federation (FSSF-2020-0018).

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Correspondence to V. A. Popov.

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Popov, V.A. Elliptic Functional Differential Equations with Degenerations. Lobachevskii J Math 41, 869–894 (2020). https://doi.org/10.1134/S199508022005011X

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  • DOI: https://doi.org/10.1134/S199508022005011X

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