Papamikos, Georgios and Pryer, Tristan (2019) A Lie symmetry analysis and explicit solutions of the two-dimensional ∞-Polylaplacian. Studies in Applied Mathematics, 142 (1). pp. 48-64. DOI https://doi.org/10.1111/sapm.12232
Papamikos, Georgios and Pryer, Tristan (2019) A Lie symmetry analysis and explicit solutions of the two-dimensional ∞-Polylaplacian. Studies in Applied Mathematics, 142 (1). pp. 48-64. DOI https://doi.org/10.1111/sapm.12232
Papamikos, Georgios and Pryer, Tristan (2019) A Lie symmetry analysis and explicit solutions of the two-dimensional ∞-Polylaplacian. Studies in Applied Mathematics, 142 (1). pp. 48-64. DOI https://doi.org/10.1111/sapm.12232
Abstract
In this work, we consider the Lie point symmetry analysis of a strongly nonlinear partial differential equation of third order, the ∞‐Polylaplacian, in two spatial dimensions. This equation is a higher order generalization of the ∞‐Laplacian, also known as Aronsson's equation, and arises as the analog of the Euler–Lagrange equations of a second‐order variational principle in L∞. We obtain its full symmetry group, one‐dimensional Lie subalgebras and the corresponding symmetry reductions to ordinary differential equations. Finally, we use the Lie symmetries to construct new invariant ∞‐Polyharmonic functions.
Item Type: | Article |
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Additional Information: | 13 pages |
Uncontrolled Keywords: | fully nonlinear partial differential equations; invariant solutions; Lie symmetries; infinity-Polylaplacian; variational calculus |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 05 Nov 2020 13:30 |
Last Modified: | 30 Oct 2024 16:32 |
URI: | http://repository.essex.ac.uk/id/eprint/26459 |
Available files
Filename: A Lie symmetry analysis and explicit solutions of the two dimensional inf-polylaplacian.pdf