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Converse spectral problems for nodal domains. (English) Zbl 1125.35068
From the abstract: “We consider two-dimensional Schrödinger operators in bounded domains. Abstractions of nodal sets are introduced and spectral conditions for them ensuring that they are actually zero sets of eigenfunctions are given. This is illustrated by an application to optimal partitions.”

MSC:
35P05 General topics in linear spectral theory for PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35J10 Schrödinger operator, Schrödinger equation
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