On a stochastic wave equation in two space dimensions: regularity of the solution and its density

We pursue the investigation started in a recent paper by Millet and Sanz-So le (1999, Ann. Probab. 27, 803-844) concerning a non-linear wave equation d riven by a Gaussian white noise in time and correlated in the two-dimension al space variable. Under more restrictive conditions on the covariance func tion of the noise, we prove Holder-regularity properties for both the solut ion and its density. For the latter, we adapt the method used in a paper by Morien (1999, Bernoulli: Official J. Bernoulli Sec. 5(2), 275-298) based o n the Malliavin calculus. (C) 2000 Elsevier Science B.V. All rights reserve d.