A necessary condition for the regularity of a boundary point for degenerating parabolic equations with measurable coefficients
We prove a necessary condition for the regularity of a point on a cylindrical boundary for solutions of second-order quasilinear parabolic equations of divergent form whose coefficients have a superlinear growth relative to derivatives with respect to space variables. This condition coincides with t...
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| Datum: | 2004 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2004
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3801 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509933517144064 |
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| author | Skrypnik, I. I. Скрыпник, И. И. Скрыпник, И. И. |
| author_facet | Skrypnik, I. I. Скрыпник, И. И. Скрыпник, И. И. |
| author_sort | Skrypnik, I. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:09:24Z |
| description | We prove a necessary condition for the regularity of a point on a cylindrical boundary for solutions of second-order quasilinear parabolic equations of divergent form whose coefficients have a superlinear growth relative to derivatives with respect to space variables. This condition coincides with the sufficient condition proved earlier by the author. Thus, we establish a criterion for the regularity of a boundary point similar to the well-known Wiener criterion for the Laplace equation. |
| first_indexed | 2026-03-24T02:48:58Z |
| format | Article |
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| id | umjimathkievua-article-3801 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:48:58Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/12/90d7faf7d37435d9bc330db1c8a11212.pdf |
| spelling | umjimathkievua-article-38012020-03-18T20:09:24Z A necessary condition for the regularity of a boundary point for degenerating parabolic equations with measurable coefficients Необходимое условие регулярности граничной точки для вырождающихся параболических уравнений с измеримыми коэффициентами Skrypnik, I. I. Скрыпник, И. И. Скрыпник, И. И. We prove a necessary condition for the regularity of a point on a cylindrical boundary for solutions of second-order quasilinear parabolic equations of divergent form whose coefficients have a superlinear growth relative to derivatives with respect to space variables. This condition coincides with the sufficient condition proved earlier by the author. Thus, we establish a criterion for the regularity of a boundary point similar to the well-known Wiener criterion for the Laplace equation. Доведено необхідну умову регулярності точки на циліндричній границі для розв'язків квазілінійних параболічних рівнянь другого порядку дивергентної форми, коефіцієнти яких мають надлінійний ріст відносно похідних за просторовими змінними. Ця умова збігається з достатньою умовою, доведеною раніше автором. Тим самим отримано критерій регулярності граничної точки, аналогічний відомому критерію Вінера для рівняння Лапласа. Institute of Mathematics, NAS of Ukraine 2004-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3801 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 6 (2004); 818–836 Український математичний журнал; Том 56 № 6 (2004); 818–836 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/3801/4322 https://umj.imath.kiev.ua/index.php/umj/article/view/3801/4323 Copyright (c) 2004 Skrypnik I. I. |
| spellingShingle | Skrypnik, I. I. Скрыпник, И. И. Скрыпник, И. И. A necessary condition for the regularity of a boundary point for degenerating parabolic equations with measurable coefficients |
| title | A necessary condition for the regularity of a boundary point for degenerating parabolic equations with measurable coefficients |
| title_alt | Необходимое условие регулярности граничной точки для вырождающихся параболических уравнений с измеримыми коэффициентами |
| title_full | A necessary condition for the regularity of a boundary point for degenerating parabolic equations with measurable coefficients |
| title_fullStr | A necessary condition for the regularity of a boundary point for degenerating parabolic equations with measurable coefficients |
| title_full_unstemmed | A necessary condition for the regularity of a boundary point for degenerating parabolic equations with measurable coefficients |
| title_short | A necessary condition for the regularity of a boundary point for degenerating parabolic equations with measurable coefficients |
| title_sort | necessary condition for the regularity of a boundary point for degenerating parabolic equations with measurable coefficients |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3801 |
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