We study the regularity of Kirchhoff equations defined on an open bounded domain (\Omega, \operatorname{dim} \Omega=1,2,3), and subject to the action of point control (through the Dirac mass (\delta) ) at an interior point of (\Omega). The results of this paper are " (\frac{1}{2}+\varepsilon) " sharper in space regularity, measured in Sobolev space order, over those that can be obtained by simply using that, by Sobolev embedding, (\delta \in\left[H^{x}(\Omega)\right], x=\frac{3}{2}+\varepsilon) for (N=3, x=1+\varepsilon) for (N=2, x=\frac{1}{2}+8) for (N=1). The approach used here is very general. ' 1993 Academic Press. Inc
Contents.
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Introduction, statement of the problem. 1.1. Statement of the problem and literature. 1.2. A preliminary estimate for Kirchhoff problems.
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Kirchhoff equation with homogencous houndary conditions (\left.\left.n\right|{2} \equiv \mathbf{d} u\right|{2} \equiv 0) and interior point control. 2.1. Statement of results. 2.2. Proof of Theorem 2.1.
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Kirchhoff equation with homogeneous Dirichlet Neumann houndary conditions (\left(\left.w\right|{\Sigma}=\left.(\mathrm{in} / \mathrm{v})\right|{2} \equiv 0\right)) and interior point control. 3.1. Statement of results. 3.2. Proof of Theorem 3.1.