i am recently starting my studies on solutions of elliptic pde's of second order in the sense of viscosity. From this study some doubts result, they are:
- What is the motivation to introduce a new type of solution for a pde, besides the classic sense and weak sense?
- What are the limitations that are overcome in finding viscosity solutions that other methods cannot provide?
- What to break from the classical theory of dust when looking for solutions via viscosity?
- Is there any physical interpretation for a viscosity solution?