NEW YORK — Norsk Film’s psychological thriller “Insomnia,” the Stellan Skarsgard starrer that received critical acclaim in Cannes, will make its U.S. premiere at the second annual Nantucket Film Festival, which runs June 17-22 on the Massachusetts isle.Now in its second year, the fest has recently attracted the support of Viacom’s Showtime Networks Inc., which joins such sponsors as BankBoston, Vanity Fair, Avid Technology, Champagne Mumm and Writers Guild of America East. The Nantucket fest is trying to carve out a niche for itself by celebrating writing. Toward this end, Showtime is sponsoring the Tony Cox Award for Screenwriting in honor of the former Showtime chairman and CEO, who died last year of a heart attack. Cox was a summer resident of Nantucket and provided informal advice to film festival executive director Jonathan Burkhart when he was trying to launch the fest. “It seems appropriate that the Nantucket Film Festival honor Tony, whose values and conviction were consistent with the tenets of this award,” said Showtime chairman and CEO Matthew C. Blank. “The creation of an award with Tony Cox’s name will serve as a living memorial to a man who believed in excellence.” More than 500 submissions have been received for the screenplay competition. After the entries have been narrowed to down to six finalists by a staff of 40 readers, the winner will be chosen by a jury that includes writer-director Darnell Martin; National Public Radio film critic David D’Arcy; Roland Legiardi Laura of Gotham’s Nuyorican Poets Cafe; producer-director Peter Cohn; producer Nancy Tennenbaum; and “The Daytrippers” writer-director Greg Mottola. In addition to “Insomnia,” this year’s Nantucket Film Festival includes 18 features, 21 shorts and five staged readings of new screenplays. “The slate this year reflects what we consider to be some of today’s best screenwriting,” said fest co-founder and artistic director Jill Goode.