Here is the perfect and natural way to clean a burnt stainless steel pan without too much effort.
Put a 1/1 water and vinegar composition, enough to completely cover the burnt area on your stainless steel pan. Put the pan over medium heat and let the water burn for 10-15 minutes, or until the burn unsticks when you scratch it with a wooden spoon.
After 15 minutes, more than 90% of the traces should disappear and the remaining ones will be much easier to remove with a regular sponge and detergent.
It is necessary to ventilate the room well when using this procedure, as vinegar vapors can be very irritating to the respiratory system.
The method works very well especially for stainless steel saucepans.