Accessibility navigation


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

[img]
Preview
Text - Accepted Version
· Please see our End User Agreement before downloading.

335kB

It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

To link to this item 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
Refereed:Yes
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:79792
Publisher:Massachusetts Institute of Technology

Downloads

Downloads per month over past year

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation