A weighted gradient estimate for solutions of $ L^p $ Christoffel-Minkowski problem
We extend the weighted gradient estimate for solutions of nonlinear PDE associated to the prescribed $ k $-th $ L^p $-area measure problem to the case $ 0 < p < 1 $. The estimate yields non-collapsing estimate for symmetric convex bodied with prescribed $ L^p $-area measures.
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-09-01
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| Series: | Mathematics in Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2023067?viewType=HTML |
| _version_ | 1797659068475637760 |
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| author | Pengfei Guan |
| author_facet | Pengfei Guan |
| author_sort | Pengfei Guan |
| collection | DOAJ |
| description | We extend the weighted gradient estimate for solutions of nonlinear PDE associated to the prescribed $ k $-th $ L^p $-area measure problem to the case $ 0 < p < 1 $. The estimate yields non-collapsing estimate for symmetric convex bodied with prescribed $ L^p $-area measures. |
| first_indexed | 2024-03-11T18:08:38Z |
| format | Article |
| id | doaj.art-caef8b34902748fba2419d3f4fa71983 |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-03-11T18:08:38Z |
| publishDate | 2023-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-caef8b34902748fba2419d3f4fa719832023-10-17T01:14:54ZengAIMS PressMathematics in Engineering2640-35012023-09-015311410.3934/mine.2023067A weighted gradient estimate for solutions of $ L^p $ Christoffel-Minkowski problemPengfei Guan0Department of Mathematics and Statistics, McGill University, Montreal, H3A 0B9, CanadaWe extend the weighted gradient estimate for solutions of nonlinear PDE associated to the prescribed $ k $-th $ L^p $-area measure problem to the case $ 0 < p < 1 $. The estimate yields non-collapsing estimate for symmetric convex bodied with prescribed $ L^p $-area measures.https://www.aimspress.com/article/doi/10.3934/mine.2023067?viewType=HTMLarea measureschristoffel-minkowski problemconstant rank theorem |
| spellingShingle | Pengfei Guan A weighted gradient estimate for solutions of $ L^p $ Christoffel-Minkowski problem Mathematics in Engineering area measures christoffel-minkowski problem constant rank theorem |
| title | A weighted gradient estimate for solutions of $ L^p $ Christoffel-Minkowski problem |
| title_full | A weighted gradient estimate for solutions of $ L^p $ Christoffel-Minkowski problem |
| title_fullStr | A weighted gradient estimate for solutions of $ L^p $ Christoffel-Minkowski problem |
| title_full_unstemmed | A weighted gradient estimate for solutions of $ L^p $ Christoffel-Minkowski problem |
| title_short | A weighted gradient estimate for solutions of $ L^p $ Christoffel-Minkowski problem |
| title_sort | weighted gradient estimate for solutions of l p christoffel minkowski problem |
| topic | area measures christoffel-minkowski problem constant rank theorem |
| url | https://www.aimspress.com/article/doi/10.3934/mine.2023067?viewType=HTML |
| work_keys_str_mv | AT pengfeiguan aweightedgradientestimateforsolutionsoflpchristoffelminkowskiproblem AT pengfeiguan weightedgradientestimateforsolutionsoflpchristoffelminkowskiproblem |