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Full-Text Articles in Physical Sciences and Mathematics
Remarks On The One-Dimensional Sloshing Problem Involving The $P$-Laplacian Operator, Wei-Chuan Chen, Yanhsiou Cheng
Remarks On The One-Dimensional Sloshing Problem Involving The $P$-Laplacian Operator, Wei-Chuan Chen, Yanhsiou Cheng
Turkish Journal of Mathematics
In this paper, we study the inverse nodal problem and the eigenvalue gap for the one-dimensional sloshing problem with the $p$-Laplacian operator. By applying the Prüfer substitution, we first derive the reconstruction formula of the depth function by using the information of the nodal data. Furthermore, we employ the Tikhonov regularization method to consider how to reconstruct the depth function using only zeros of one eigenfunction. Finally, we investigate the eigenvalue gap under the restriction of symmetric single-well depth functions. We show the gap attains its minimum when the depth function is constant.
Mixed Boundary Value Problem For A Class Of Quasi-Linear Elliptic Operators Containing $P$-Laplacian, Junichi Aramaki
Mixed Boundary Value Problem For A Class Of Quasi-Linear Elliptic Operators Containing $P$-Laplacian, Junichi Aramaki
Turkish Journal of Mathematics
In this paper, we consider a mixed boundary value problem to a class of quasi-linear elliptic operators containing a $p$-Laplace operator. We show the existence of a unique weak solution and an estimate. We also demonstrate the continuity of the solution on the given data. Moreover, we consider the dual problem.