Background  Gotham Steel is a ceramic coated titanium pan.  It's the brand with the commercials where they put a mixer in the pan, supposedly to show that it doesn't scratch if you use metal utensils.  The coating makes the pan non-stick, slippery even.    It comes with the following instructions:       FOR BEST PERFORMANCE      Gotham Steel™ Ti-Cerama™ Cookware with Titanium Ceramic Coating is designed for cooking without oil or butter.  If you choose to use oil or butter, always use it at the proper heat setting.  For example, extra virgin olive oil and butter should only be used over low heat.  NEVER USE NON STICK SPRAYS.  No sharp objects of any type should be used on the inside or outside of Ti-Cerama™ cookware.     (Emphasis in original.)  I take the last sentence to mean that the mixer ad is exaggerated, but that's not my question.    Olive Oil and coated pans  It says to only use extra virgin olive oil with "low" heat.  Since that's not exactly precise, I searched around for more information.  Some reviews said that Le Creuset (which makes a similar, enamel coated iron pan) says not to use olive oil at all.  So some people that had both recommended the same thing for the Gotham Steel pans.  No olive oil at all.    I found this question and this question that suggest that the issue might be extra virgin olive oil's low smoke point.  I.e. that the olive oil might simply be susceptible to burning.  Not sure why the coating would make that worse, but it's a hypothesis.    What actually happens when using olive oil on these kinds of pans?  Preferably Gotham Steel, but I'd take information on Le Creuset or similar brands of enamel/ceramic coated cookware.  What's "low" heat in this context?    Example  I sometimes cook sandwich eggs in a Teflon pan with a little olive oil.  This basically involves turning the Kenmore stove to 7, letting the oil heat as I scramble an egg in a cup.  I turn the head down to 4 and pour the egg into the pan.  I wait until the egg is almost cooked through and then flip it.  I turn off the heat and wait a bit longer, then I eat it in a sandwich.  My experience is that if I do it right, the egg is fully cooked without fry marks.    The stovetop is a Kenmore electric with the flat glass on top.  Non-induction, a regular heating element.  The heat goes Lo-2-3-4-Med-6-7-8-Hi.  The obvious thing would be for "low" heat to be Lo on the stovetop.  However, that's not a heat that I would normally use for anything other than simmering for a long period of time.  E.g. making rice.  Does 4 count as "low" heat since I don't keep it there long?    Anyway, if I did that same process with the Gotham Steel pan, what would happen?  Would it ruin the pan?  Burn the egg?  Burn the oil?    Note that if I don't use the oil, it cooks the egg fine and it slides right out of the pan.  That's satisfactory, but I would prefer to understand why I should or should not use olive oil.    Ideally someone would have a scientific answer with testing using a Gotham Steel pan.  However, I would take an anecdotal answer involving a Le Creuset or other brand if it was explanatory.  E.g. I tried that with a ____ and boy did it ruin the pan by ...  Other oils  What happens with other greases and oils?  For example, we tried cooking a meatloaf in the dutch oven sized pan.  The ceramic container that we normally use is getting old and could be bigger.  So we were curious if this would work.  We normally use a fatty ground beef and pour off the grease before eating.  This leaves the bottom rather soft.  However, with this pan, the result was that the bottom charred into a black crunchiness.  Is this related to the problem with olive oil?  Or something entirely different and worthy of its own question?  Same thing with the passage about non stick sprays.    The instructions say that the oven is safe to 500 degrees Fahrenheit.  We cooked at 350.  That's about 175-180 in metric/Celsius.    We also tried a couple roasts in water with sliced onions underneath and they baked fine.  And we tried a casserole that has lentils, rice, and Swiss cheese.  That's rather greasy, but it didn't have the same behavior as the meatloaf.  I.e. the edges touching the pan didn't scorch or char.    How do I know which oils will be problematic and which won't?   
You can fry in olive oil as long as you exercise some care. Some olive oils have smoke points of 400 F.  If you know how to cook, you can even do it by eye (anyone that lets oil go past its smoke point once or twice can control it so that doesn't happen again).  Anyway, I cook with olive oil in my Gotham Steel pan and dutch oven all the time, no problem.  I also have a degree in chemical engineering and I understand what happens with polymerization - yes Virginia, you can avoid the gunky mess.  By the way, if it does happen, don't try to muscle away polymerized gunky oil.  A little hot/steamy water and rubbing alcohol does wonders.  