But there is no "the" inhomogeneous solution, and indeed there cannot be. That is the whole point. One can only distinguish between inhomogeneous solutions by the imposition of boundary conditions. This is a fundamental mathematical inevitability.
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Interesting, but irrelevant to our discussion. In that paper Dirac tries to solve the problem of the field singularity for a point electron within the Maxwell eqs framework, but it never claims (like you do) that classical electrodynamics is nonlocal.
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Sigh. Did you read the paper? All of its conclusions depend upon choices of Green functions, which in turn depend upon boundary conditions. Physical laws do not determine boundary conditions. Imposing them in general, which you are doing, is adding a non-local law to physics.
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