Regularity with Interior Point Control. Part II. Kirchhoff Equations

We study the regularity of Kirchhoff equations defined on an open bounded domain Ω, dim Ω = 1, 2, 3, and subject to the action of point control (through the Dirac mass δ) at an interior point of Ω. The results of this paper are " + ε" sharper in space regularity, measured in Sobolev space order, over those that can be obtained by simply using that, by Sobolev embedding, δ [Hα(Ω)]′, α + ε for N = 3, α = l + ε for N = 2, α = + ε for N = l. The approach used here is very general.