What is the chemical structure of ceramic nonstick coating on pans?
There is a near continuum (and thus a potential infinitude) of relative concentrations of the different components of ceramics and their means of fabrication, but US Patent US7879449 B2 (PDF) gives a thorough description of their own non-stick ceramic invention as well as descriptions and references to others.  Below are several excerpts from the cited patent:

The novel coating includes a $\ce{SiO2}$ ceramic matrix that includes the condensation product of hydrolyzed alkoxysilane and a colloidal silica sol. A series of new abrasion resistant and high hardness non-stick coating materials have been developed with ceramic matrix and organic compounds by sol-gel process.
This non-stick material has two main component of silicon dioxide. One is silica sol which is pure $\ce{SiO2}$, another is an organoalkoxysilane which is an organic-inorganic hybrid material. Both materials can make strong chemical bond from chemical reaction, condensation. $\ce{(OR')_{4-x}}$ groups are hydrolyzed with water and then make condensation with silica sol and each other. The ceramic non-stick hybrid coating is applied by a sol-gel process. Two kinds of non-stick organic compounds make a chemical bond with silica ceramic network or matrix and it can exist in the ceramic structure in a stable state.
The main matrix is composed of a network of silica formed by the chemical reaction or condensation of colloidal silica sol (water base) and an organoalkoxysilane such as MTMS (methyltrimethoxysilane). The colloidal silica sol is a very stable state because of the electrostatic repulsion of silica particle surface.
The organoalkoxysilane preferably has the general formula $\ce{R_xSi(OR')_{4-x}}$. Wherein $\ce{R}$ is one or more organic radicals chosen independently from among methyl, ethyl, and propyl, $\ce{R'}$ is a low molecular weight alkyl radical, and x is at least one and less than four. Commonly x is one, so that the organoalkoxysilane has three hydrolysable sites. This increases cohesion and bonding of the components and also provides a thickened layer and increases the links with the inorganic silica surface.
The surface of colloidal silica is coated by organoalkoxysilanes, in other words, hydrolyzed organoalkoxysilane make a thin layer or coating on the silica surface as a result of the condensation reaction with the hydroxyl groups of the silica surface.

Again, this is just an overview of a single process. The patent is well written and diagrammed and I suggest reading in detail to best answer your question (Images &gt; Full Pages).