Geodesic
The $\infty(x)$-Laplace equation in Riemannian vector fields
Electronic Journal of Differential Equations, Tome 2015 (2015).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We employ Riemannian jets which are adapted to the Riemannian geometry to obtain the existence-uniqueness of viscosity solutions to the $infinity(x)$-Laplace equation in Riemannian vector fields. Due to the differences between Euclidean jets and Riemannian jets, the Euclidean method of proof is not valid in this environment.
Classification : 35H20, 53C17, 49L25, 31B05, 31C12
Keywords: viscosity solution, Riemannian vector field, infinite Laplacian 
@article{EJDE_2015__2015__a90,
     author = {Bieske, Thomas},
     title = {The $\infty(x)${-Laplace} equation in {Riemannian} vector fields},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a90/}
}
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Bieske, Thomas. The $\infty(x)$-Laplace equation in Riemannian vector fields. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a90/