How can Restylane cause downturned lip corners when smiling, can it be fixed?

A downturned smile or permanent frown can be improved with a combination approach, including neuromodulators (such as Botox, Dysport, and Jeuveau), injectable fillers, and radiofrequency skin tightening treatments such as Thermage or Venus Legacy. I recommend getting a formal evaluation with an experienced cosmetic dermatologist to develop a treatment plan that works for you. Best, Dr. Emer.

I am sorry that you are experiencing this problem. Without photos and a bit more information about exactly where the material was injected, I can only comment in general terms. What I can say is that treating the angles of the mouth is an advanced injection technique that should best be performed by very experienced injectors and not novice injectors accustomed to treating ordinary smile lines with simple Restylane. By contrast, downturned corners of the mouth or full-blown marionette lines require addressing individual anatomic differences, rather than a cookbook approach. For some people proper treatment would mean treating aging, flattening cheeks with a volumizing filler, such as Voluma XC or Restylane Lyft. For others, it may mean providing direct support to the tissue immediately below the corners of the mouth to elevate and buttress these areas. And for still others, this may mean treatment above and below, both to elevate and support. If about a month has passed since your treatment, then it would be wise to see your treating physician. Alternatively, you may seek a second opinion from a board certified aesthetic physician with experience and expertise in advanced injection techniques for treating this region, and make certain to ask to see his/her before and after photos. Best of luck. 

After 2-3 weeks swelling will subside and you can make a decision as to whether you want this product dissolved with hyaluronidase or if you want it to get metabolized on its own over time. Go back to the physician who did the injections for follow up advice or correction.BestH Karamanoukian MD FACS

Without photographs we can only speculate on possible treatment for your problem.
There are three possibilities to manage  this problem.  The first is to do your best to ignore it, knowing that the filler material will disappear over the upcoming months.  The second is that your downturn may be improved by carefully adding additional filler.  Finally, the hyaluronic acid gel can be disolved by injection of hyaluronidase.  Suggest that you are examined by physician who will help you decide how to manage your lips

When volume is placed in the lip there is pressure to turn down the corners of the lip with movement and this can be fixed with Botox injected into the DAO muscle

Thank you for your question. If you are unhappy with your injections there are a couple of options - 1) more may help to even things out, or to make you look more natural with expressions 2) the filler that you have can be dissolved with something called hyaluronidase. The last option, of course, is to do nothing - and just realize that things should settle out over time. In fact, as your face adjusts to having the filler, there is a good chance that things will just naturally settle out in time - probably in a couple weeks. I would suggest speaking with the person who injected you; or, ask this question again this time with photos and we can do our best to advise you. Good luck! 

You should post photos. It could depend a lot on your normal anatomy and your age.  More information would be needed to answer this more accurately.