Symmetry and Convexity of Level Sets of Solutions to the Infinity Laplace's Equation
Date
1998-12-09
Authors
Rosset, Edi
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We consider the Dirichlet problem
-Δ∞u = ƒ(u) in Ω,
u = 0 on ∂Ω,
where Δ∞u = uxi, uxj, uxi xj and ƒ is a nonnegative continuous function. We investigate whether the solutions to this equation inherit geometrical properties from the domain Ω. We obtain results concerning convexity of level sets and symmetry of solutions.
Description
Keywords
Infinity-Laplace equation, p-Laplace equation
Citation
Rosset, E. (1998). Symmetry and convexity of level sets of solutions to the infinity Laplace's equation. <i>Electronic Journal of Differential Equations, 1998,</i>(34), pp. 1-12.
Rights
Attribution 4.0 International