It's physically impossible to glue Teflon. You can roughen the surface and use contact adhesive and it WILL stay put of a few minutes but as soon as any load is applied it will slip and move.
Staple/ fine large headed nails/ screws etc are unfortunately the only way to go.
Don't know about frying pans!!!!!
"To move beyond mere mechanics, the frying-pan engineers added a sticky molecule to the non-stick molecule. Non-stick was now applied in coats, with the bottom coat containing the sticky additive that held to both the metal pan and the non-stick molecules. A coat of non-sticky non-stick went over that, non-stick and non-stick clinging together lovingly. A final non-stick layer, spiked with teensy bits of ceramic or other tougheners, protected the softer guts".
You must use Etched Teflon.
It has been acid etched and then can be guled with contact adhesive. The best way is to Glue and Screw.
If you have Virgin Teflon the best way is to countersink screw it.