The Corcoran Gallery of Art has received a valentine from the Mobil Corporation: Starting in mid-May the Corcoran will be open on Sunday evenings until 9. The museum now closes at 4:30 p.m. every day.

Mobil will foot the bill for the additional staff and utility costs, but declined to reveal the amount of the grant. For several years, Mobil has supported free Tuesday nights at the Whitney and Guggenheim museums in New York, increasing Tuesday attendance by 50 percent. The company has also sponsored "Summergarden" at the Museum of Modern Art, free weekend evenings of music and dance during summer months in MOMA's sculpture garden.

"We will be planning several special events for Sunday evenings," Corcoran director Peter Marzio said yesterday. In addition to lectures, tours and artist demonstration, "During the summer there will be puppet performances and puppet-making seminars, and in the fall, a series of jazz performances is being planned," he said.

"What's important," Marzio said, "is that here we have a private corporation keeping a private museum open. The Smithsonian museum stay open nights during the summer, but at public expense."

The National Gallery is the only Washington museum now open on Sunday nights year round.

"Maybe Sunday will become museum night in Washington," said Marzio. "And it should work, given all those empty downtown parking spaces on Sunday evenings."