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Solutions for equations involving the infinity-Laplacian. (English) Zbl 1397.35008

Summary: In this paper, we study a parabolic equation involving the infinity-Laplacian from the point of view of Lie symmetries. We consider its radial form and, by using the method of separation of variables, we derive another one involving the Aronsson’s nonlinear operator. All Lie point symmetries of these equations are found and by using the invariance group we are able to find exact solutions for the considered equations, some of them expressed in terms of the hypergeometric function.

MSC:

35A30 Geometric theory, characteristics, transformations in context of PDEs
58J70 Invariance and symmetry properties for PDEs on manifolds
70G65 Symmetries, Lie group and Lie algebra methods for problems in mechanics
35J60 Nonlinear elliptic equations
35J70 Degenerate elliptic equations

Software:

SYM
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References:

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