A symmetry problem in the calculus of variations
Copyright policy )A symmetry problem in the calculus of variations
We consider a class of integral functionals defined in a Sobolev space of functions vanishing at the boundary of a nonempty bounded connected open n-dimensional set. We prove that, if the functional admits a minimizer depending only on the distance from the boundary, then that set must be a ball.
calculus of variations, symmetry of solutions, Optimality conditions for problems involving partial differential equations, Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces, distance function, Optimal control problems with differential inclusions (nec./ suff.), Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
calculus of variations, symmetry of solutions, Optimality conditions for problems involving partial differential equations, Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces, distance function, Optimal control problems with differential inclusions (nec./ suff.), Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
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