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math. opérateur {m} laplacien [aussi : laplacien] | Laplace operator [also: Laplacian] |

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Usage Examples English

- 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 distribution is a constant multiple of that density distribution. - thesis, "Curvature and Eigenforms of the
**Laplace Operator**" ("Journal of Differential Geometry"), and "An Analytical Proof of the Riemann-Roch-Hirzebruch Formula for Kaehler Manifolds" (also "Journal of Differential Geometry"), Patodi made his fundamental breakthroughs. - Since the
**Laplace operator**appears in the heat equation, one physical interpretation of this problem is as follows: fix the temperature on the boundary of the domain according to the given specification of the boundary condition. - In general, the mass measure "dm" can be recovered in the same way if the
**Laplace operator**is taken in the sense of distributions. - Because the Klein quartic has the largest symmetry group of surfaces in its topological class, much like the Bolza surface in genus 2, it has been conjectured that it maximises the first positive eigenvalue of the
**Laplace operator**among all compact Riemann surfaces of genus 3 with constant negative curvature.

- The most studied isospectral problem in infinite dimensions is that of the
**Laplace operator**on a domain in R2. - This generalizes the case of 3-dimensional Euclidean space, in which divergence of a vector field may be realized as the codifferential opposite to the gradient operator, and the
**Laplace operator**on a function is the divergence of its gradient. - can be seen as the kernel of the
**Laplace operator**[...] and is therefore a vector space over [...] linear combinations of harmonic functions are again harmonic. - Example: The
**Laplace operator**in "k" variables has symbol [...] , and so is elliptic as this is nonzero whenever any of the [...] 's are nonzero. - In the physics literature, the
**Laplace operator**is often denoted by [...]; in the mathematics literature, [...] may also denote the Hessian matrix of [...].

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