Geodesic
Fundamental solutions to the \(p\)-Laplace equation in a class of Grushin vector fields
Electronic journal of differential equations, Tome 2011 (2011)
We find the fundamental solution to the p-Laplace equation in a class of Grushin-type spaces. The singularity occurs at the sub-Riemannian points, which naturally corresponds to finding the fundamental solution of a generalized Grushin operator in Euclidean space. We then use this solution to find an infinite harmonic function with specific boundary data and to compute the capacity of annuli centered at the singularity.
Classification : 35H20, 53C17, 17B70
Keywords: Grushin-type spaces, p-Laplacian 
@article{EJDE_2011__2011__a51,
     author = {Bieske,  Thomas},
     title = {Fundamental solutions to the {\(p\)-Laplace} equation in a class of {Grushin} vector fields},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1225.35060},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a51/}
}
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Bieske,  Thomas. Fundamental solutions to the \(p\)-Laplace equation in a class of Grushin vector fields. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a51/