Elliptic and Parabolic Equations with Involution and Degeneration at Higher Derivatives

Aleksandr I. Kozhanov () and Oksana I. Bzheumikhova
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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

Mathematics, 2022, vol. 10, issue 18, 1-10

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.

Keywords: elliptic equation; parabolic equation; boundary value problem; involution; degeneration; regular solution; existence; uniqueness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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