I read here the following:
The parametrix is a useful concept in the study of elliptic differential operators and, more generally, of hypoelliptic pseudodifferential operators with variable coefficient, since for such operators over appropriate domains a parametrix can be shown to exist, can be somewhat easily constructed and be a smooth function away from the origin. Having found the analytic expression of the parametrix, it is possible to compute the solution of the associated fairly general elliptic partial differential equation by solving an associated Fredholm integral equation: also, the structure itself of the parametrix reveals properties of the solution of the problem without even calculating it, like its smoothness and other qualitative properties.
Does anyone know any reference (books/papers) where I can find more infomation about using parametrix and Fredholm integral equations for attacking hypoellipticity problems?
Thanks
