Geodesic
Symmetry and convexity of level sets of solutions to the infinity Laplace's equation
Electronic journal of differential equations, Tome 1998 (1998)
Zbl   EuDML
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 
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/
@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},
     year = {1998},
     volume = {1998},
     zbl = {0911.35010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a31/}
}
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