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Surface Delta Function
In potential theory (a branch of mathematics), the Laplacian of the indicator is obtained by letting the Laplace operator work on the indicator function of some domain (mathematics), domain ''D''. It is a generalisation of the derivative (mathematics), derivative (or "prime function") of the Dirac delta function to higher dimensions; it is non-zero only on the surface (mathematics), surface of ''D''. It can be viewed as a ''surface delta prime function'', the derivative of a ''surface delta function'' (a generalization of the Dirac delta). The Laplacian of the indicator is also analogous to the second derivative of the Heaviside step function in one dimension. 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''. Therefore, it is not strictly a function (mathematics), function but a generalized function or measure (mathematics), measure. Similarly to the derivative of the Dirac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplacian Of The Indicator V2
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a Scalar field, scalar function on Euclidean space. It is usually denoted by the symbols \nabla\cdot\nabla, \nabla^2 (where \nabla is the Del, nabla operator), or \Delta. In a Cartesian coordinate system, the Laplacian is given by the sum of second partial derivatives of the function with respect to each independent variable. In other coordinate systems, such as cylindrical coordinates, cylindrical and spherical coordinates, the Laplacian also has a useful form. Informally, the Laplacian of a function at a point measures by how much the average value of over small spheres or balls centered at deviates from . The Laplace operator is named after the French mathematician Pierre-Simon de Laplace (1749–1827), who first applied the operator to the study of celestial mechanics: the Laplacian of the gravitational potential due to a given mass density distributio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
