English: Scan via Heritage Auctions Lot #36334. Cropped from the original image.

English: Published by Random House. Jacket design by George Salter.

English: No permission is required for two reasons:

1. First, the image is a mechanical scan that does not constitute a work of original authorship in and of itself (i.e., it is a faithful reproduction of the cover itself without modification).
2. Second, the dust jacket passed into the public domain because it was published in the United States prior to 1978 without a valid copyright notice.

Atlas Shrugged was first published in 1957; the hardcover book itself carried a copyright notice, so its contents remain copyrighted. However, dust jackets were required to carry a separate copyright notice for independent protection of their design. According to The Compendium of U.S. Copyright Office Practices: Chapter 2200, § 2207.1(C) at p. 15:

"A notice of copyright on the dust jacket of a book is not an acceptable notice for the book, because the dust jacket is not permanently attached to the book. Likewise, a notice appearing in a book is not an acceptable notice for the dust jacket or any material appearing on that dust jacket, even if the book refers to the jacket or material appearing on the jacket."

Keep in mind that the pre-1989 requirements for copyright notice were highly formalistic and, other than a few enumerated exceptions, required these three elements:

1. "The symbol © or the word 'Copyright' or the abbreviation 'Copr.' or an acceptable variant such as "(c)";
2. "The year of first publication for the work"; and
3. "The name of the copyright owner, or an abbreviation by which the name can be recognized, or a generally known alternative designation of the owner."

If just one of these elements is omitted, the work is deemed to be published without notice and is not eligible for copyright protection. The dust jacket did not include a valid notice with all of these elements; neither a copyright symbol nor the year of publication appear.