Short of a surgical "corner of mouth lift", which is an option, using strategic placement of filler injections to support the lateral lip is effective, as is judicious and accurate placement of Botox in the muscles that pull the corners of the mouth downward (these muscles are call the depressor anguli oris muscles or DAO muscles) is effective as well.
Hello. Nonsurgical options such as injectables may treat the frown lines successfully in some cases. Others require a true operation to get the job done. A midface lift is one of the smaller type of surgical procedures that can be done to do this. I recommend you seek the advice of a plastic surgeon to determine which option is right for you.