Elliptic and Parabolic Equations with Involution and Degeneration at Higher Derivatives
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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-09-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/18/3325 |
| _version_ | 1827659176470380544 |
|---|---|
| author | Aleksandr I. Kozhanov Oksana I. Bzheumikhova |
| author_facet | Aleksandr I. Kozhanov Oksana I. Bzheumikhova |
| author_sort | Aleksandr I. Kozhanov |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T23:15:51Z |
| format | Article |
| id | doaj.art-a79fdf4d54b145f9bdc3ab119122dd79 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:15:51Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a79fdf4d54b145f9bdc3ab119122dd792023-11-23T17:36:40ZengMDPI AGMathematics2227-73902022-09-011018332510.3390/math10183325Elliptic and Parabolic Equations with Involution and Degeneration at Higher DerivativesAleksandr I. Kozhanov0Oksana I. Bzheumikhova1Sobolev Institute of Mathematics, Acad. Koptyug Av. 4, 630090 Novosibirsk, RussiaDepartment of Algebra and Differential Equations, Kabardino-Balkarian State University Named after H.M. Berbekov, Chernyshevskogo St. 173, 360004 Nalchik, RussiaWe 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.https://www.mdpi.com/2227-7390/10/18/3325elliptic equationparabolic equationboundary value probleminvolutiondegenerationregular solution |
| spellingShingle | Aleksandr I. Kozhanov Oksana I. Bzheumikhova Elliptic and Parabolic Equations with Involution and Degeneration at Higher Derivatives Mathematics elliptic equation parabolic equation boundary value problem involution degeneration regular solution |
| title | Elliptic and Parabolic Equations with Involution and Degeneration at Higher Derivatives |
| title_full | Elliptic and Parabolic Equations with Involution and Degeneration at Higher Derivatives |
| title_fullStr | Elliptic and Parabolic Equations with Involution and Degeneration at Higher Derivatives |
| title_full_unstemmed | Elliptic and Parabolic Equations with Involution and Degeneration at Higher Derivatives |
| title_short | Elliptic and Parabolic Equations with Involution and Degeneration at Higher Derivatives |
| title_sort | elliptic and parabolic equations with involution and degeneration at higher derivatives |
| topic | elliptic equation parabolic equation boundary value problem involution degeneration regular solution |
| url | https://www.mdpi.com/2227-7390/10/18/3325 |
| work_keys_str_mv | AT aleksandrikozhanov ellipticandparabolicequationswithinvolutionanddegenerationathigherderivatives AT oksanaibzheumikhova ellipticandparabolicequationswithinvolutionanddegenerationathigherderivatives |