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A symmetry problem in the calculus of variations

Graziano Crasta (2006)

Journal of the European Mathematical Society

We consider the integral functional J ( u ) = Ω [ f ( | D u | ) u ] d x , u W 0 1 , 1 ( Ω ) , where Ω n , n 2 , is a nonempty bounded connected open subset of n with smooth boundary, and s f ( | s | ) is a convex, differentiable function. We prove that if J admits a minimizer in W 0 1 , 1 ( Ω ) depending only on the distance from the boundary of Ω , then Ω must be a ball.

Affine invariants of annuli

Waldemar Cieślak, Elżbieta Szczygielska (2012)

Annales UMCS, Mathematica

A family of regular annuli is considered. Affine invariants of annuli are introduced.

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