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Elliptic and Parabolic Equations with Involution and Degeneration at Higher Derivatives

Author

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  • Aleksandr I. Kozhanov

    (Sobolev Institute of Mathematics, Acad. Koptyug Av. 4, 630090 Novosibirsk, Russia)

  • Oksana I. Bzheumikhova

    (Department of Algebra and Differential Equations, Kabardino-Balkarian State University Named after H.M. Berbekov, Chernyshevskogo St. 173, 360004 Nalchik, Russia)

Abstract

We study the solvability in Sobolev spaces of boundary value problems for elliptic and parabolic equations with variable coefficients in the presence of an involution (involutive deviation) at higher derivatives, both in the nondegenerate and degenerate cases. For the problems under study, we prove the existence theorems as well as the uniqueness of regular solutions, i.e., those that have all weak derivatives in the equation.

Suggested Citation

  • Aleksandr I. Kozhanov & Oksana I. Bzheumikhova, 2022. "Elliptic and Parabolic Equations with Involution and Degeneration at Higher Derivatives," Mathematics, MDPI, vol. 10(18), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3325-:d:914436
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    References listed on IDEAS

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    1. Ulyana Yarka & Solomiia Fedushko & Peter Veselý, 2020. "The Dirichlet Problem for the Perturbed Elliptic Equation," Mathematics, MDPI, vol. 8(12), pages 1-14, November.
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