Top 10 similar words or synonyms for laplace_operator

laplacian    0.867046

scalar_curvature    0.862710

hilbert_transform    0.849307

laplace_beltrami_operator    0.848161

heaviside_step_function    0.843721

dirac_delta_function    0.843609

laplace_transform    0.839148

legendre_transform    0.828431

euler_lagrange_equation    0.826853

dirac_operator    0.822569

Top 30 analogous words or synonyms for laplace_operator

Article Example
Laplace operator As a second-order differential operator, the Laplace operator maps functions to functions for . The expression (or equivalently ) defines an operator , or more generally an operator for any open set .
Laplace operator Since this holds for all smooth regions , it can be shown that this implies
Laplace operator If denotes the electrostatic potential associated to a charge distribution , then the charge distribution itself is given by the negative of the Laplacian of :
Laplace operator This is a consequence of Gauss's law. Indeed, if is any smooth region, then by Gauss's law the flux of the electrostatic field is proportional to the charge enclosed:
Laplace operator Another motivation for the Laplacian appearing in physics is that solutions to in a region are functions that make the Dirichlet energy functional stationary: