en.wikipedia.org/wiki/Laplace's_equation

In mathematics, Laplace's equation is a second-order partial differential equation
named after Pierre-Simon Laplace who first studied its properties. This is often ...

tutorial.math.lamar.edu/Classes/DE/LaplacesEqn.aspx

We can see that Laplace's equation would correspond to finding the equilibrium
solution (i.e. time independent solution) if there were not sources. So, this is an ...

mathworld.wolfram.com/LaplacesEquation.html

A solution to Laplace's equation is uniquely determined if (1) the value of the
function is specified on all boundaries (Dirichlet boundary conditions) or (2) the ...

www.robots.ox.ac.uk/~jmb/lectures/pdelecture5.pdf

Laplace's Equation. • Separation of variables – two examples. • Laplace's
Equation in Polar Coordinates. – Derivation of the explicit form. – An example
from ...

hyperphysics.phy-astr.gsu.edu/hbase/electric/laplace.html

LaPlace's and Poisson's Equations. A useful approach to the calculation of
electric potentials is to relate that potential to the charge density which gives rise
to it.

web.mit.edu/6.013_book/www/chapter5/5.4.html

Having investigated some general properties of solutions to Poisson's equation, it
is now appropriate to study specific methods of solution to Laplace's equation ...

web.stanford.edu/class/math220b/handouts/laplace.pdf

to solve Poisson's equation. Given the symmetric nature of Laplace's equation,
we look for a radial solution. That is, we look for a harmonic function u on Rn
such ...

www.mathpages.com/home/kmath214/kmath214.htm

Typically we are given a set of boundary conditions and we need to solve for the (
unique) scalar field j that is a solution of the Laplace equation and that satisfies ...

newton.ex.ac.uk/teaching/CDHW/EM/CW970317-2.pdf

1. Analytic Solutions to Laplace's Equation in 2-D. Cartesian Coordinates. When
it works, the easiest way to reduce a partial differential equation to a set of ...

www.math.ubc.ca/~peirce/M257_316_2012_Lecture_24.pdf

Key Concepts: Laplace's equation; Steady State boundary value problems in two
or more dimensions; Linearity;. Decomposition of a complex boundary value ...