Lecture 21

Abstract

An integral equation of the form

$$ \int\limits_\Gamma {K(x,y) } u (y) d\sigma (y) = f(x), x \in \Gamma , $$

is said, rather formally, to be of the first kind, while that of the form

$$ u(x) + \int\limits_\Gamma {K(x,y) } u (y) d\sigma (y) = f(x), x \in \Gamma , $$

is said to be of the second kind. Here, dσ is the arc length element. In the operator form, we write Ku = f and (I + K)u = f, respectively.