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- Q6488263 subject Q7036100.
- Q6488263 subject Q8482201.
- Q6488263 subject Q8612084.
- Q6488263 abstract "In mathematics, the Laplacian of the indicator of the domain D is a generalisation of the derivative of the Dirac delta function to higher dimensions, and is non-zero only on the surface of D. It can be viewed as the surface delta prime function. It is analogous to the second derivative of the Heaviside step function in one dimension. It can be obtained by letting the Laplace operator work on the indicator function of some domain D.The Laplacian of the indicator can be thought of as having infinitely positive and negative values when evaluated very near the boundary of the domain D. From a mathematical viewpoint, it is not strictly a function but a generalized function or measure. Similarly to the derivative of the Dirac delta function in one dimension, the Laplacian of the indicator only makes sense as a mathematical object when it appears under an integral sign; i.e. it is a distribution function. Just as in the formulation of distribution theory, it is in practice regarded as a limit of a sequence of smooth functions; one may meaningfully take the Laplacian of a bump function, which is smooth by definition, and let the bump function approach the indicator in the limit.".
- Q6488263 thumbnail Laplacian_of_the_indicator_v2.jpg?width=300.
- Q6488263 wikiPageWikiLink Q1143737.
- Q6488263 wikiPageWikiLink Q1154848.
- Q6488263 wikiPageWikiLink Q1217677.
- Q6488263 wikiPageWikiLink Q1379273.
- Q6488263 wikiPageWikiLink Q1544810.
- Q6488263 wikiPageWikiLink Q192276.
- Q6488263 wikiPageWikiLink Q203484.
- Q6488263 wikiPageWikiLink Q209675.
- Q6488263 wikiPageWikiLink Q2381860.
- Q6488263 wikiPageWikiLink Q26336.
- Q6488263 wikiPageWikiLink Q273176.
- Q6488263 wikiPageWikiLink Q273328.
- Q6488263 wikiPageWikiLink Q322339.
- Q6488263 wikiPageWikiLink Q338886.
- Q6488263 wikiPageWikiLink Q361254.
- Q6488263 wikiPageWikiLink Q371983.
- Q6488263 wikiPageWikiLink Q466720.
- Q6488263 wikiPageWikiLink Q47480.
- Q6488263 wikiPageWikiLink Q5300057.
- Q6488263 wikiPageWikiLink Q7036100.
- Q6488263 wikiPageWikiLink Q846537.
- Q6488263 wikiPageWikiLink Q8482201.
- Q6488263 wikiPageWikiLink Q8612084.
- Q6488263 wikiPageWikiLink Q865811.
- Q6488263 wikiPageWikiLink Q944.
- Q6488263 comment "In mathematics, the Laplacian of the indicator of the domain D is a generalisation of the derivative of the Dirac delta function to higher dimensions, and is non-zero only on the surface of D. It can be viewed as the surface delta prime function. It is analogous to the second derivative of the Heaviside step function in one dimension.".
- Q6488263 label "Laplacian of the indicator".
- Q6488263 depiction Laplacian_of_the_indicator_v2.jpg.