In applied mathematics, the Calderón projector is a pseudo-differential operator used widely in boundary element methods. It is named after Alberto Calderón.
Definition The interior Calderón projector is defined to be:
where is almost everywhere, is the identity boundary operator, is the double layer boundary operator, is the single layer boundary operator, is the adjoint double layer boundary operator and is the hypersingular boundary operator; on a given bounded domain with compact boundary .
The exterior Calderón projector on a complementary domain (taking its interior) is defined to be:
That is also linked to the interior Calderón projector by .
Calderón identities
As the Calderón operator is a projector; that means that , the following identities holds :
References