Determining Sets for the Discrete Laplacian

• Autores: Aviad Rubinstein, Jacob Rubinstein, Gershon Wolansky
• Localización: SIAM Review, ISSN 0036-1445, Vol. 49, Nº. 2, 2007, págs. 315-324
• Idioma: inglés
• DOI: 10.1137/050645233
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• Resumen

  • We define a notion of determining sets for the discrete Laplacian in a domain O . A set $D$ is called determining if harmonic functions are uniquely determined by providing their values on $D$, and if $D$ has the same size as the boundary of O. It is shown that there exist determining sets that are fairly evenly distributed in O. A number of basic properties of determining sets are derived.