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An Introduction to Partial Differential Equations by Jacob Rubinstein, Yehuda Pinchover

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8

Green’s functions and integral representations

8.1 Introduction

Integral representations play a central role in various fields of pure and applied mathematics, theoretical physics, and engineering. Many boundary value problems and initial boundary value problems can be solved using integral kernels. In such a case, we usually have an explicit formula for the solution as a (finite) sum of integrals involving integral kernels and the associated side conditions (which are the given data). The integral kernel depends on the differential operator, the type of given boundary condition, and the domain. It should be computed just once for any given type of problem. Hence, given an integral representation for a differential problem, we can find the ...

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