"existing work of" is correct and can be used in written English.
It is usually used when referring to an already existing body of work. For example: "This research paper attempts to build on the existing work of other scholars in the field."
Our analysis builds on the existing work of Hoge et al [ 2] and suggests that different sets of barriers exist for different common mental disorders.
In other words: adapting for television an existing work of science fiction was impossible and hiring any science-fiction writer inadvisable.
(Catsoulis) Film Series The Complete Howard Hawks (Saturday and Sunday) The Museum of the Moving Image continues its complete retrospective of the existing work of Howard Hawks.
Frears's The Burning centres on a violent insurrection in southern Africa as observed by a young white boy; unlike the other films, it's based on an existing work of some distinction.
Mr. Ostlund said he did not know whether National Electric Vehicle would tap the existing work of the ePower program, but noted that the company planned to utilize "Japanese electric vehicle technology and expertise".
Jain et al. [18] reviewed the existing work of fingerprint template protection such as encryption, template transformation, and crypto-biometric systems.
Stability of a moving boundary at which fog forms or vaporizes is analyzed using techniques of existing work on stability of moving solid surfaces.
Most of the existing work on fatigue of long fiber composite laminates approach the problem from the material point of view.
Conditional Ka/Ks represents a slight extension of existing work on co-evolution of amino acid residues in protein sequences.
Existing work on annotation of relations addresses only a limited number of relation types in the biomedical domain.
A lot of existing work on innovation is mainly concerned with improving the work of NGOs and international organisations.
