We consider the problem of finding Steklov eigenfunctions with constant gradient's modulus on the boundary of a planar domain. We show that the domain cannot be arbitrarily given. In fact, we give a way to construct such domains as images of suitable conformal mappings.
Symmetry and non-symmetry for the overdetermined Stekloff eigenvalue problem / R. MAGNANINI; ALESSANDRI G.NI. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK. - ISSN 0044-2275. - STAMPA. - 45:(1994), pp. 44-52.
Symmetry and non-symmetry for the overdetermined Stekloff eigenvalue problem
MAGNANINI, ROLANDO;
1994
Abstract
We consider the problem of finding Steklov eigenfunctions with constant gradient's modulus on the boundary of a planar domain. We show that the domain cannot be arbitrarily given. In fact, we give a way to construct such domains as images of suitable conformal mappings.
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