What You (Can't) Do About It
Really... there's not a whole lot that can be done, on your part. Pixel vignetting is something that is, for the moment, more-or-less inherent in digital cameras.
Because the amount of pixel vignetting that occurs is constant given a certain camera design, there has been some effort to create automatic processing techniques to remove the pixel vignetting effect when the image is being converted from a RAW to a JPEG or other file format.
There has also been an effort by camera companies to design microlenses that fit over the image sensor that will refract light so that it strikes head on across the entire image sensor. This could, in theory, alleviate all angle-dependent types of vignetting, including not only pixel vignetting but also natural and optical vignetting. However, as of the writing of this article, this is neither commonplace, nor entirely perfected. Stay tuned!
While pixel vignetting tends to be subtle, and often only detectable when compounded by other types of vignetting such as optical and natural vignetting, you can still try to amend it. Careful use of digital editing software can help alleviate the effects of pixel vignetting, either by darkening the center of the image to match the edges, or the opposite, by lightening the edges to match the center.
Check out Types of Vignetting: What are The Different Causes of Vignetting? to learn more about vignetting as it relates to photography.