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Volume 39, Issue 3
Interior Gradient Estimates for General Prescribed Curvature Equations

Zhenan Sui & Wei Sun

Anal. Theory Appl., 39 (2023), pp. 260-286.

Published online: 2023-09

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  • Abstract

In this paper, we derive the interior gradient estimate for solutions to general prescribed curvature equations. The proof is based on a fundamental observation of Gårding's cone and some delicate inequalities under a suitably chosen coordinate chart. As an application, we obtain a Liouville type theorem.

  • AMS Subject Headings

53C21

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COPYRIGHT: © Global Science Press

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@Article{ATA-39-260, author = {Sui , Zhenan and Sun , Wei}, title = {Interior Gradient Estimates for General Prescribed Curvature Equations}, journal = {Analysis in Theory and Applications}, year = {2023}, volume = {39}, number = {3}, pages = {260--286}, abstract = {

In this paper, we derive the interior gradient estimate for solutions to general prescribed curvature equations. The proof is based on a fundamental observation of Gårding's cone and some delicate inequalities under a suitably chosen coordinate chart. As an application, we obtain a Liouville type theorem.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2022-0025}, url = {http://global-sci.org/intro/article_detail/ata/22001.html} }
TY - JOUR T1 - Interior Gradient Estimates for General Prescribed Curvature Equations AU - Sui , Zhenan AU - Sun , Wei JO - Analysis in Theory and Applications VL - 3 SP - 260 EP - 286 PY - 2023 DA - 2023/09 SN - 39 DO - http://doi.org/10.4208/ata.OA-2022-0025 UR - https://global-sci.org/intro/article_detail/ata/22001.html KW - Interior gradient estimate, prescribed curvature equations. AB -

In this paper, we derive the interior gradient estimate for solutions to general prescribed curvature equations. The proof is based on a fundamental observation of Gårding's cone and some delicate inequalities under a suitably chosen coordinate chart. As an application, we obtain a Liouville type theorem.

Sui , Zhenan and Sun , Wei. (2023). Interior Gradient Estimates for General Prescribed Curvature Equations. Analysis in Theory and Applications. 39 (3). 260-286. doi:10.4208/ata.OA-2022-0025
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