We derive an analytic, albeit approximate, expression for the ground state energy of N Coulomb interacting anyons with fractional statistics nu, 0less than or equal to than or equal to1, 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 cutoff parameter to existing exact analytical results in the noninteracting case, and to numerical calculations for electrons in quantum dots in the interacting case. The resulting expression depends upon parameters of the system 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 a comparison with exact, approximate, and numerical results from the literature.