Answer: It's difficult to get grass to grow under oak trees. The shade presents a problem because grasses prefer to grow in full sun, but the soil is also dry beneath trees and tree roots will compete for moisture and nutrients. You can overseed the area each spring with a shade tolerant grass seed or you can give up on the lawn and plant a shade loving ground cover. One of the more common plants we use in the shade is Monkey Grass. The standard type of Monkey Grass gradually spreads and in fact, can end creeping it's way out into your lawn. There's a dwarf type that really works well, especially among walking stones. It stays extremely low. You can maybe mow it once a year to keep it fresh. It's an excellent choice for the shade.
Another common plant is liriope. Liriope comes in a standard green form, there's the regular type and one that gets even taller. And then there's some variegated forms of liriope as well. There's also a relative of liriope and Monkey Grass called Aztec Grass. It has white and green striped leaves that really brightens up the shade very well.
Best wishes with your landscape!
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