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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

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To link to this item DOI: 10.1111/sapm.12232


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
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:79792
Publisher:Massachusetts Institute of Technology


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