Regularity of a Boundary Point for Degenerate Parabolic Equations with Measurable Coefficients
We investigate the continuity of solutions of quasilinear parabolic equations in the neighborhood of the nonsmooth boundary of a cylindrical domain. As a special case, one can consider the equation \(\frac{{\partial u}}{{\partial t}} - \Delta _p u = 0\) with the p-Laplace operator Δp. We prove a...
Saved in:
| Date: | 2000 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2000
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4560 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510704364158976 |
|---|---|
| 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 | 2020-03-18T20:31:24Z |
| description | We investigate the continuity of solutions of quasilinear parabolic equations in the neighborhood of the nonsmooth boundary of a cylindrical domain. As a special case, one can consider the equation \(\frac{{\partial u}}{{\partial t}} - \Delta _p u = 0\) with the p-Laplace operator Δp. We prove a sufficient condition for the regularity of a boundary point in terms of C p-capacity. |
| first_indexed | 2026-03-24T03:01:14Z |
| format | Article |
| fulltext |
0110
0111
0112
0113
0114
0115
0116
0117
0118
0119
0120
0121
0122
0123
|
| id | umjimathkievua-article-4560 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:01:14Z |
| publishDate | 2000 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/5b/1af75c16191879cce44bcac75d7d9a5b.pdf |
| spelling | umjimathkievua-article-45602020-03-18T20:31:24Z Regularity of a Boundary Point for Degenerate Parabolic Equations with Measurable Coefficients Регулярность граничной точки для вырождающихся параболических уравнений с измеримыми коэффициентами Skrypnik, I. I. Скрыпник, И. И. Скрыпник, И. И. We investigate the continuity of solutions of quasilinear parabolic equations in the neighborhood of the nonsmooth boundary of a cylindrical domain. As a special case, one can consider the equation \(\frac{{\partial u}}{{\partial t}} - \Delta _p u = 0\) with the p-Laplace operator Δp. We prove a sufficient condition for the regularity of a boundary point in terms of C p-capacity. Досліджується неперервність розв'язків квазілінійних параболічних рівнянь біля негладкої границі циліндричної області. Як частинний випадок можна розглядати рівняння-$\frac{{\partial u}}{{\partial t}} - \Delta _p u = 0$ з оператором $p$-Лапласа $Δp$. Доведено достатню умову регулярності граничної точки в термінах $С_р$ -ємності. Institute of Mathematics, NAS of Ukraine 2000-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4560 Ukrains’kyi Matematychnyi Zhurnal; Vol. 52 No. 11 (2000); 1550-1565 Український математичний журнал; Том 52 № 11 (2000); 1550-1565 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4560/5824 https://umj.imath.kiev.ua/index.php/umj/article/view/4560/5825 Copyright (c) 2000 Skrypnik I. I. |
| spellingShingle | Skrypnik, I. I. Скрыпник, И. И. Скрыпник, И. И. Regularity of a Boundary Point for Degenerate Parabolic Equations with Measurable Coefficients |
| title | Regularity of a Boundary Point for Degenerate Parabolic Equations with Measurable Coefficients |
| title_alt | Регулярность граничной точки для вырождающихся параболических
уравнений с измеримыми коэффициентами |
| title_full | Regularity of a Boundary Point for Degenerate Parabolic Equations with Measurable Coefficients |
| title_fullStr | Regularity of a Boundary Point for Degenerate Parabolic Equations with Measurable Coefficients |
| title_full_unstemmed | Regularity of a Boundary Point for Degenerate Parabolic Equations with Measurable Coefficients |
| title_short | Regularity of a Boundary Point for Degenerate Parabolic Equations with Measurable Coefficients |
| title_sort | regularity of a boundary point for degenerate parabolic equations with measurable coefficients |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4560 |
| work_keys_str_mv | AT skrypnikii regularityofaboundarypointfordegenerateparabolicequationswithmeasurablecoefficients AT skrypnikii regularityofaboundarypointfordegenerateparabolicequationswithmeasurablecoefficients AT skrypnikii regularityofaboundarypointfordegenerateparabolicequationswithmeasurablecoefficients AT skrypnikii regulârnostʹgraničnojtočkidlâvyroždaûŝihsâparaboličeskihuravnenijsizmerimymikoéfficientami AT skrypnikii regulârnostʹgraničnojtočkidlâvyroždaûŝihsâparaboličeskihuravnenijsizmerimymikoéfficientami AT skrypnikii regulârnostʹgraničnojtočkidlâvyroždaûŝihsâparaboličeskihuravnenijsizmerimymikoéfficientami |