A characterization of the ellipsoid through the torsion problem

GRECO, ANTONIO

2008-01-01

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Abstract

The solution u of the torsion problem in an N-dimensional bounded domain is investigated. The ratio of the partial derivative ∂u/∂x_N to the variable x_N is assumed to satisfy a suitable condition along the boundary. If the projection of the domain onto the hyperplane { x_N = 0 } is an (N−1)-dimensional ellipsoid, then the domain itself must be an ellipsoid symmetric in x_N in order that the problem is solvable.