As the title suggests, I am kinda struggling to understand the basic idea behind viscosity solutions theory. The theorems are a lot different from what I saw in classical theory for PDEs (with Sobolev, Morrey, Campanato spaces, decay properties etc). They are in a certain way more "abstract", and I kinda find hard to get an idea of what is really going on. It's not that I don't understand some passages of proofs, it's just that I fail to get a view on the "bigger picture", if you know what I mean.
Do you know some introductory notes on the topic, or can you provide some insight? I am not searching for something rigorous, I just want to undersand the idea behind this theory.
