Revision #836 → #1345 · back to history
addedLaplace operator (informal)3eba00eef616
addedHarmonic function3b9be979cfe9
addedLaplacian as divergence of gradient84143a3739a7
addedLaplacian as sum of unmixed second partialse8cc2ed3d38c
addedLaplacian maps C^k to C^{k-2}7ca1698464db
addedLaplacian via sphere averages83cfdd00c9fc
addedNegative semidefinite sign conventionb70b0be55152
addedNonnegative sign convention4929b201aa6a
addedDiffusion equilibrium and Laplace's equation31fc66f52eb8
addedDiffusion implies Laplace's equationb4626012f5a0
addedAverage over a ball811379d0b5be
addedAverage over a sphere2ec46e8bc097
addedCharge density from electrostatic potential20527fb4d0ff
addedGauss's law derivation2b75cd3d2ade
addedMass distribution from gravitational potential3c2ec2267625
addedHarmonic functions minimize Dirichlet energy583a70c7c634
addedDirichlet stationary iff harmonic733a31f83770
addedLaplacian in 2D Cartesian coordinates56a27caa553b
addedLaplacian in polar coordinates783f4fe3543b
addedLaplacian in 3D Cartesian coordinates1598dc9a3bb5
addedLaplacian in cylindrical coordinateseea1b0b981cb
addedLaplacian in spherical coordinates5b26ce8822c6
addedLaplacian in general curvilinear coordinates (3D)c51827e78731
addedLaplacian in N-dim curvilinear coordinatesc4c623dcb09f
addedRadial/angular decomposition of Laplacian5c68f003ded0
addedSpherical harmonic eigenvalue equationc7e9df6c61db
addedRadial equation and solid harmonics0352b1eea21d
addedRadial harmonic functions on annulusa80963ccc12d
addedSpherical Laplacian via homogeneous extensiond2bd6d4e8586
addedEuclidean equivariance of Laplacianb303304fd03f
addedRotation/translation invariance in 2D98a195137c9d
addedEuclidean group invarianceb34290fb155a
addedCharacterization of Euclidean-invariant operatorsf94d0d19eeb6
addedAngular Laplacian as Casimire1a924730772
addedLaplace–Beltrami from Casimir on homogeneous spaces1279e7039d48
addedLinearity of the Laplacian6f0f9d14d1dc
addedEllipticity of the Laplacian80ee10b356ed
addedGreen's identities for the Laplaciancb675e5ae9d7
addedFormal self-adjointnessb911f0ef8c79
addedEnergy identity6edc136b2269
addedHarmonic, subharmonic, superharmonic6b5dff3fa0a7
addedMean value property8dfe8c96a16d
addedMaximum and minimum principles5f5be9e5fc6c
addedElliptic regularity for the Laplacian063064ec989a
addedSmoothness/analyticity of harmonic functions2c33cc8cbd84
addedWeyl's lemma15f834a7a9d1
addedLaplacian as Fourier multiplier464f44cd940d
addedHeat semigroup and fractional powers via Fourierc070bd89a4ec
addedContinuous spectrum on R^n495c16f17a42
addedDiscrete spectrum on bounded domainsbb1898f46d22
addedHelmholtz equation2990a0bcd98e
addedSpectrum of Laplace–Beltrami on compact manifold32b59f5d6b97
addedFractional Laplacian (Fourier definition)5a5769f04fbf
addedFractional Laplacian (singular integral)8d8f241db241
addedRiesz potential59115628c3ed
addedBessel potential0e0118fbce3e
addedVector Laplaciane47a2cfce7a0
addedVector Laplacian via Helmholtz decompositionf6751cc2cb10
addedVector Laplacian in Cartesian coordinatesb47ce7de8181
addedTensor Laplacian2d7fb6705846
addedNavier–Stokes equation3413fc99101c
addedWave equation for electric field824479c1357d
addedHeat semigroupdf768dde4edb
addedSmoothing effect of heat semigroupe1308eec9394
addedHeat kernel on manifolds4ad4b3e625d3
addedLaplace–Beltrami operator1f51d2124abb
addedGeometer's Laplacian8d58f9539548
addedHodge Laplacian / Laplace–de Rhamf6e091c5f8ec
addedD'Alembert operator5755f26a9ad4