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.
Brandolini, B. (2013). On the Symmetry of Solutions to a k-Hessian Type Equation. ADVANCED NONLINEAR STUDIES, 13(2), 487-493.
On the Symmetry of Solutions to a k-Hessian Type Equation
Brandolini, B
2013-01-01
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.
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