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  "body": "\n## Summary\n\nA fundamental solution of a linear differential operator $P$ is a distribution $E$ with $P E = \\delta$, the Dirac delta at the origin.\nFor an operator with constant coefficients, convolving $E$ with a source $f$ gives a solution of $P u = f$.\nFundamental solutions are the Green's functions of the whole space, and they underlie potential theory, the [[heat kernel|KD404MF042]] and the theory of wave propagation.\nSee the [[definition|ZY724M2NKQ]].\n\n## Explanations\n\n### L1 human\n\nA fundamental solution is the response of a physical system to a point source.\nFor gravity or electrostatics in space, the potential of a point mass is proportional to $1/\\abs{x}$.\nUp to a constant factor, this function is the fundamental solution of the Laplace operator.\nA general mass distribution is a sum of point masses, so its potential is a sum, or integral, of shifted copies of $1/\\abs{x}$.\nThat is why one fundamental solution solves the equation for all sources.\n",
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