scholarly journals Derivations of the Young-Laplace equation

Capillarity ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 23-30
Author(s):  
Leiv Magne Siqveland ◽  
Svein Magne Skjaeveland
Keyword(s):  
2020 ◽  
Vol 18 (1) ◽  
pp. 1685-1697
Author(s):  
Zhenyu Zhao ◽  
Lei You ◽  
Zehong Meng

Abstract In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method.


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