The infinite dimensional Green measure g is shown to be a product measure and this provides sufficient conditions for the existence and the differentiability of potentials. Moreover, it is shown how such conditions can be used to prove that if f is Lip and if we set u = Gf, then first D2u is Lip too and second u satisfies Δu = -2f for a wide class of functions f with arbitrary support.
|Original language||English (US)|
|Number of pages||17|
|Journal||Journal of Functional Analysis|
|State||Published - Nov 1977|
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