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- Laplacian_of_the_indicator 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.".
- Laplacian_of_the_indicator thumbnail Laplacian_of_the_indicator_v2.jpg?width=300.
- Laplacian_of_the_indicator wikiPageID "37670148".
- Laplacian_of_the_indicator wikiPageLength "28272".
- Laplacian_of_the_indicator wikiPageOutDegree "45".
- Laplacian_of_the_indicator wikiPageRevisionID "708184734".
- Laplacian_of_the_indicator wikiPageWikiLink Bump_function.
- Laplacian_of_the_indicator wikiPageWikiLink Category:Generalized_functions.
- Laplacian_of_the_indicator wikiPageWikiLink Category:Mathematics_of_infinitesimals.
- Laplacian_of_the_indicator wikiPageWikiLink Category:Measure_theory.
- Laplacian_of_the_indicator wikiPageWikiLink Characteristic_function.
- Laplacian_of_the_indicator wikiPageWikiLink Delta_potential.
- Laplacian_of_the_indicator wikiPageWikiLink Dirac_delta_function.
- Laplacian_of_the_indicator wikiPageWikiLink Distribution_(mathematics).
- Laplacian_of_the_indicator wikiPageWikiLink Divergence_theorem.
- Laplacian_of_the_indicator wikiPageWikiLink Double_layer_potential.
- Laplacian_of_the_indicator wikiPageWikiLink Electrostatics.
- Laplacian_of_the_indicator wikiPageWikiLink File:Laplacian_of_the_indicator_v2.jpg.
- Laplacian_of_the_indicator wikiPageWikiLink Fundamental_theorem_of_calculus.
- Laplacian_of_the_indicator wikiPageWikiLink Generalized_function.
- Laplacian_of_the_indicator wikiPageWikiLink Greens_identities.
- Laplacian_of_the_indicator wikiPageWikiLink Heaviside_step_function.
- Laplacian_of_the_indicator wikiPageWikiLink Indicator_function.
- Laplacian_of_the_indicator wikiPageWikiLink Integration_by_parts.
- Laplacian_of_the_indicator wikiPageWikiLink Laplace_operator.
- Laplacian_of_the_indicator wikiPageWikiLink Measure_(mathematics).
- Laplacian_of_the_indicator wikiPageWikiLink Normal_(geometry).
- Laplacian_of_the_indicator wikiPageWikiLink Paul_Dirac.
- Laplacian_of_the_indicator wikiPageWikiLink Potential_theory.
- Laplacian_of_the_indicator wikiPageWikiLink Product_rule.
- Laplacian_of_the_indicator wikiPageWikiLink Quantum_mechanics.
- Laplacian_of_the_indicator wikiPageWikiLink Surface_area.
- Laplacian_of_the_indicator wikiPageWikiLinkText "Laplacian of the indicator".
- Laplacian_of_the_indicator wikiPageWikiLinkText "inward normal derivative of the indicator".
- Laplacian_of_the_indicator wikiPageWikiLinkText "surface delta function".
- Laplacian_of_the_indicator wikiPageUsesTemplate Template:Disambiguation_needed.
- Laplacian_of_the_indicator wikiPageUsesTemplate Template:Mvar.
- Laplacian_of_the_indicator wikiPageUsesTemplate Template:Reflist.
- Laplacian_of_the_indicator wikiPageUsesTemplate Template:Technical.
- Laplacian_of_the_indicator subject Category:Generalized_functions.
- Laplacian_of_the_indicator subject Category:Mathematics_of_infinitesimals.
- Laplacian_of_the_indicator subject Category:Measure_theory.
- Laplacian_of_the_indicator hypernym Generalisation.
- Laplacian_of_the_indicator type Type.
- Laplacian_of_the_indicator type Field.
- Laplacian_of_the_indicator type Function.
- Laplacian_of_the_indicator type Type.
- Laplacian_of_the_indicator 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.".
- Laplacian_of_the_indicator label "Laplacian of the indicator".
- Laplacian_of_the_indicator sameAs Q6488263.
- Laplacian_of_the_indicator sameAs m.0pdnn9y.
- Laplacian_of_the_indicator sameAs Q6488263.
- Laplacian_of_the_indicator wasDerivedFrom Laplacian_of_the_indicator?oldid=708184734.
- Laplacian_of_the_indicator depiction Laplacian_of_the_indicator_v2.jpg.
- Laplacian_of_the_indicator isPrimaryTopicOf Laplacian_of_the_indicator.
