並列摘要
We consider the Dirichlet problem for the constant mean curvature surface equation on domains with boundary data zero. We give sufficient conditions for the existence of smooth solutions provided that the boundary satisfies a certain exterior circle condition. A feature of the work is the use of pieces of nodoids as barriers to make C0 and C1 a priori estimates respectively.
參考文獻
[BC] J.L.Barbosa and M.P. do Carmo, A proof of a general isoperimetric inequality for
[CH] R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. II, Interscience,
New York, 1962
[Co] P. Collin, Deux exemples de graphes de courbure moyenne constante sur une bande
[ER] R. Earp and H. Rosenberg, The Dirichlet problem for the minimal surface equation
延伸閱讀
- Lee, K. W. (2010). 緊緻流形間的均曲率流與施瓦西時空上的常均曲率超曲面 [doctoral dissertation, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2010.03021
- Lin, Y. C. (2009). 平面曲線的曲率流及其相關問題 [doctoral dissertation, National Tsing Hua University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0016-1111200916013267
- Lin, S. M. (2015). 常均曲率方程解之唯一性以特定邊界值出發 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU201700788
- Gabeleh, M., & Shahzad, N. (2013). Existence and Convergence Theorems of Best Proximity Points. Journal of Applied Mathematics, 2013(), 21-26-002. https://doi.org/10.1155/2013/101439
- HADZIC, O. (1987). ON COINCIDENCE THEOREMS FOR A FAMILY OF MAPPINGS IN CONVEX METRIC SPACES. International Journal of Mathematics and Mathematical Sciences, 1987(), 453-460. https://doi.org/10.1155/S016117128700053X