On a partially overdetermined problem in a cone
Christos Sourdis
TL;DR
This paper proves a rigidity result for an overdetermined boundary value problem within cones, extending previous low-dimensional results to arbitrary dimensions using a new approach.
Contribution
It generalizes known results for Serrin's problem in cones to higher dimensions with a novel proof technique.
Findings
Rigidity result for Serrin's overdetermined problem in cones
Extension of low-dimensional results to arbitrary dimensions
New approach for proving overdetermined boundary value problems
Abstract
We prove a rigidity result for Serrin's overdetermined problem in a cone that is contained in a half-space in arbitrary dimensions. In the special case where the cone is an epigraph, this result was shown previously in low dimensions with a different approach.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Composite Material Mechanics