Segre’s theorem. An analytic proof of a result in differential geometry

We present an analytic approach on how to solve the overdetermined problem $\lvert \nabla u \rvert = f(u), \Delta u = g(u)$, in connected domains $\Omega \subseteq \mathbb{R}^n$.

Keywords

isoparametric, viscosity, eigenprojections, $1$-Laplacian, matrix derivatives, Cartan’s fundamental formula

2010 Mathematics Subject Classification

35C05, 35J60, 53A05

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The author was supported by the Academy of Finland (grant SA13316965), and by Aalto University.

Received 13 August 2020

Accepted 28 August 2020

Published 14 March 2022