As far as I know
to the best of my knowledge
is interpreted by
pour autant que je sache
to the best of the author's knowledge
should I use
pour autant que l'auteur sache
or is it better to use
au meilleur de la connaissance de l'auteur
or another structure?
To the best of the author's knowledge is a more formal way to say as far as he or she (the author) knows. Say that one has written down something in a scientific publication. He or she has thoroughly searched the relevant literature but he or she could not find a single reference of the result in question.
The author has searched carefully but he or she cannot searched the WHOLE literature of an enormous field like, e.g. continuum mechanics. So one uses this expression. I am not a French native speaker but I thought it should not sound so awkward in French.
As a real example (taken from Freed's book: Soft Solids):
"The Eulerian velocity gradient l is typically denoted as L in the literature. That notation is reserved here for the Lagrangian velocity gradient defined in Eq. (2.24), which is a field not found in the literature to the best of the author’s knowledge."