Regularity of a boundary point for singular parabolic equations with measurable coefficients
We investigate the continuity of solutions of quasilinear parabolic equations near the nonsmooth boundary of a cylindrical domain. We prove a sufficient condition for the regularity of a boundary point, which coincides with the Wiener condition for the Laplace p-operator. The model case of the equat...
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| Дата: | 2004 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2004
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3772 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509905045159936 |
|---|---|
| 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 | 2020-03-18T20:08:07Z |
| description | We investigate the continuity of solutions of quasilinear parabolic equations near the nonsmooth boundary of a cylindrical domain. We prove a sufficient condition for the regularity of a boundary point, which coincides with the Wiener condition for the Laplace p-operator. The model case of the equations considered is the equation \(\frac{{\partial u}}{{\partial t}} - \Delta _p u = 0\) with the Laplace p-operator Δ p for 2n / (n + 1) < p < 2. |
| first_indexed | 2026-03-24T02:48:31Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-3772 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:48:31Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/5e/090326a7a22bad0c97e8e9297c5b605e.pdf |
| spelling | umjimathkievua-article-37722020-03-18T20:08:07Z Regularity of a boundary point for singular parabolic equations with measurable coefficients Регулярность граничной точки для сингулярных параболических уравнений с измеримыми коэффициентами Skrypnik, I. I. Скрыпник, И. И. Скрыпник, И. И. We investigate the continuity of solutions of quasilinear parabolic equations near the nonsmooth boundary of a cylindrical domain. We prove a sufficient condition for the regularity of a boundary point, which coincides with the Wiener condition for the Laplace p-operator. The model case of the equations considered is the equation \(\frac{{\partial u}}{{\partial t}} - \Delta _p u = 0\) with the Laplace p-operator Δ p for 2n / (n + 1) < p < 2. Досліджується неперервність розв'язків квазілінійпих параболічних рівнянь біля негладкої границі циліндричної області. Доведено достатню умову регулярності граничної точки, яка збігається з умовою Вінера для $p$-оператора Лапласа. Модельним випадком рівнянь, які розглядаються, є рівняння $$\frac{{\partial u}}{{\partial t}} - \Delta _p u = 0$$ з p$-оператором Лапласа $Δ_p$ при $2n/ (n + 1) < p < 2.$ Institute of Mathematics, NAS of Ukraine 2004-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3772 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 4 (2004); 506–516 Український математичний журнал; Том 56 № 4 (2004); 506–516 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/3772/4266 https://umj.imath.kiev.ua/index.php/umj/article/view/3772/4267 Copyright (c) 2004 Skrypnik I. I. |
| spellingShingle | Skrypnik, I. I. Скрыпник, И. И. Скрыпник, И. И. Regularity of a boundary point for singular parabolic equations with measurable coefficients |
| title | Regularity of a boundary point for singular parabolic equations with measurable coefficients |
| title_alt | Регулярность граничной точки для сингулярных параболических уравнений с измеримыми коэффициентами |
| title_full | Regularity of a boundary point for singular parabolic equations with measurable coefficients |
| title_fullStr | Regularity of a boundary point for singular parabolic equations with measurable coefficients |
| title_full_unstemmed | Regularity of a boundary point for singular parabolic equations with measurable coefficients |
| title_short | Regularity of a boundary point for singular parabolic equations with measurable coefficients |
| title_sort | regularity of a boundary point for singular parabolic equations with measurable coefficients |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3772 |
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