A Lie symmetry analysis and explicit solutions of the two-dimensional ∞-Polylaplacian

Papamikos, G. and Pryer, T. (2019) A Lie symmetry analysis and explicit solutions of the two-dimensional ∞-Polylaplacian. Studies in Applied Mathematics, 142 (1). pp. 48-64. ISSN 0022-2526 doi: 10.1111/sapm.12232

Abstract/Summary

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
URI	https://reading-clone.eprints-hosting.org/id/eprint/79792
Identification Number/DOI	10.1111/sapm.12232
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Massachusetts Institute of Technology
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