Geodesic
Symmetry and convexity of level sets of solutions to the infinity Laplace's equation
Electronic Journal of Differential Equations, Tome 1998 (1998).

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

Summary: We consider the Dirichlet problem $-\Delta_\infty u=f(u)$ in $\Omega, u=0$ on $\partial\Omega$ where $\Delta_\infty u = u_{x_i}u_{x_j}u_{x_ix_j}$ and f is a nonnegative continuous function. We investigate whether the solutions to this equation inherit geometrical properties from the domain $\Omega$. We obtain results concerning convexity of level sets and symmetry of solutions.
Classification : 35J70, 35B05
Keywords: infinity-Laplace equation, p-Laplace equation 
@article{EJDE_1998__1998__a31,
     author = {Rosset, Edi},
     title = {Symmetry and convexity of level sets of solutions to the infinity {Laplace's} equation},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {1998},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a31/}
}
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Rosset, Edi. Symmetry and convexity of level sets of solutions to the infinity Laplace's equation. Electronic Journal of Differential Equations, Tome 1998 (1998). http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a31/