PDEs and the smoothness of solutions

[defunc]

Hi all,

Suppose the solution of a pde exists and is unique, what can be said about the smoothness thereof? In general, is there some theory regarding the smoothness of the solution and its derivatives and how it depends on the boundary and boundary values? For example, if the boundary values are continuous, wil the solution always be continuous? And what can be said about the derivatives of the solution?

 

[Hootenanny]

The smoothness of a solution depends both on the boundary conditions and the classification of the PDE. See here: http://en.wikipedia.org/wiki/Partial_differential_equation#Classification (sorry that I couldn't find a better a link).

As far as I'm aware, there is no general theorem which deals with the smoothness of all unique solutions to boundary value problems.