  We derive an analytic, albeit approximate, expression for the ground state
energy of N Coulomb interacting anyons with fractional statistics nu, 0<= |nu|
<= 1, confined in a two-dimensional well (with characteristic frequency omega_0
) and subjected to an external magnetic field (with cyclotron frequency omega_c
). We apply a variational principle combined with a regularization procedure
which consists of fitting a cut-off parameter to existing exact analytical
results in the non-interacting case, and to numerical calculations for
electrons in quantum dots in the interacting case. The resulting expression
depends upon parameters of the system |nu|, N, omega_0, r_0, a_B and omega_c,
where r_0 represents a characteristic unit length and a_B the Bohr radius.
Validity of the result is critically assessed by comparison with exact,
approximate, and numerical results from the literature.
