Search results for "Hessian equations"
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Hessian equations and symmetrization
2005
In this paper we state same comparisons results for solutions to Hessian type equations in dimension n> 2. These results involve convenient rearrangements of solutions that preserve suitable cross-sectional measures of their level sets.
On the Symmetry of Solutions to a k-Hessian Type Equation
2013
Abstract In this note we prove that if u is a negative solution to a nonlinear elliptic equation involving a Hessian operator, and u is zero on the boundary of a ball, then u is radially symmetric and increasing along the radii.