Real and Complex Fundamental Solutions — A Way for Unifying Mathematical Analysis
نویسنده
چکیده
Suppose L is a differential operator of order k. Moreover, let u be a function defined and k times continuously differentiable in the closure of a domain Ω of R. Provided the adjoint differential operator possesses a fundamental solution, we shall see that u can be recovered from Lu and the boundary values of u. Strictly speaking, we shall get an integral representation of u in form of the sum of two integrals. One of them is a boundary integral, the other is a domain integral whose integrand is the product of Lu and the fundamental solution of the adjoint operator. Such integral representations can be used for solving boundary value problems.
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