No, Death Note is generally considered inappropriate for 11-year-olds.
Mature Themes and Content
Death Note contains mature themes and content not suitable for younger audiences. Several sources highlight the presence of graphic depictions of death and violence, including scenes of dead bodies and blood. The series also features instances of nudity, sexual themes, and suicide. These elements are likely to be disturbing or upsetting for an 11-year-old.
One parent explicitly stated, "it has a lot of descriptions of death and actual scenes of death & bodies, as well as guns and blood. it also has a few parts containing nudity and sexual themes. also mentions suicide. really up to the parent to decide lol but personally I wouldn't let an 11 yr old read it..." This sentiment is echoed across multiple reviews and discussions.
Many online forums and review sites advise against showing Death Note to children under 13. Common Sense Media, for example, notes the show's TV-MA/TV-14 rating, indicating its inappropriateness for younger viewers. Even discussions regarding appropriateness for 12-year-olds often suggest that 11 is too young. A Quora user notes that an 11-year-old may not fully grasp the complex and dark themes of the show.
While some argue that a mature 12-year-old might handle the content, the consensus points towards 13 as a more suitable minimum age. The complexity of the storyline, coupled with the graphic and disturbing content, makes Death Note unsuitable for most 11-year-olds.