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arXiv · 2111.09817

Existence of nonradial domains for overdetermined and isoperimetric problems in nonconvex cones

Alessandro Iacopetti·Filomena Pacella·Tobias Weth
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Abstract

In this work we address the question of the existence of nonradial domains inside a nonconvex cone for which a mixed boundary overdetermined problem admits a solution. Our approach is variational, and consists in proving the existence of nonradial minimizers, under a volume constraint, of the associated torsional energy functional. In particular we give a condition on the domain $D$ on the sphere spanning the cone which ensures that the spherical sector is not a minimizer. Similar results are obtained for the relative isoperimetric problem in nonconvex cones.

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Alessandro Iacopetti, Filomena Pacella, Tobias Weth. 2021-11-18. Existence of nonradial domains for overdetermined and isoperimetric problems in nonconvex cones. https://doi.org/10.1007/s00205-022-01801-4

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