Is there a long term treatment for gabellar lines or "eleven" lines between eyes?

In addition to botulinum toxin injections and fillers as therapy, you can also undergo an endoscopic procedure which releases the corrugator supercilii muscle. This is the muscle that causes the frown lines. This procedure is more invasive and is usually done as an addition to other procedures, but would be a more permanent solution.
Lastly, different formulations of botulinum toxin may last longer in certain patients. Their use will also prolong the life of the filler by decreasing the movement of the area.

Thank you for your question.  The only way to prevent those lines from becoming deeper is to stop the muscle movement which causes them. Neuromodulators like Botox and Dysport are the best options on the market to help you achieve that result.  You may consider adding a little filler if you are still bothered by the line after your injection treatment. There is nothing else that will work or help you.  Your dermatologist is correct, your muscles may be strong, but it may require a few treatments to get your dose just right as well potentially adding forehead area to the treatment plan to keep muscles completely relaxed and not to allow any overcompensation to happen. I always have my patients return in two weeks to reassess the dosage and movement and if higher dose is warranted, then we add it.  everyone is different and it sounds like your muscles are strong. I advise you to talk to your derm again or maybe try another provider.  Hope this helps. Best, Dr.Avaliani

Wrinkles relaxers like Botox and Dysport are the best treatments currently available for dynamic frown lines. The results typically last 3-4 months. When filler is used in this area, it is usually for "etched in" lines. Even if filler is used, it needs to be combined with Botox/Dysport or the filler will not last long. 

Thank you for your question. The best treatment for the glabellar or eleven lines, as well as to prevent them from getting deeper over time, is to stop the muscles activity that causes them with neuromodulators, like Botox. Botox last three to four months on average. Duration can be affected with improper dosing. It is always best to do a two week follow up appointment after treatment to make sure dosing is sufficient. A soft dermal filler may also be used for deeper lines in this area. However, results are longer lasting when combining filler with Botox. I hope this help. All the best, Dr. Michon

There is certainly some individual variation with duration of Botox treatment, although often after you have had treatment for a while it will last longer as the muscles take longer to recover.
As far as fillers are concerned they will generally last much longer. An ideal combination if the lines are quite deep is to combine filler with Botox. It is important that a filler in this area can be placed superficially so it needs to be soft and smooth. There will be a range of options but I like Juvederm 2 or Belotero Balance in this area.