Geodesic
The \(\infty(x)\)-Laplace equation in Riemannian vector fields
Electronic journal of differential equations, Tome 2015 (2015)
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},
     year = {2015},
     volume = {2015},
     zbl = {1327.35072},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a90/}
}
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%J Electronic journal of differential equations
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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/