Department of Mathematics
Colloquium
by
Prof. Bernard Beauzamy

Consider a simple differential equation, such as u'+u = f. If the function f is modified, how is the solution modified? This interrogation is related to stability, because in practice the data f are never known exactly. We solve this type of question for general differential operators, of the type P(D)u=f, where P is a polynomial and P(D) the associated differential operator. The tool we use for this is a new norm on polynomials (or, more generally, on some class of analytic functions), derived from Bombieri's norm. Using this norm, we can relate the variations of u to the variations of f in the above equation.

Additional References : nothing exactly on this topic. Many scattered results, for instance for elliptic operators. One may consult Hormander, Linear Partial Differential Operators, Springer Verlag.