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Optimal pointwise estimates are derived for the biharmonic Green functionunder Dirichlet boundary conditions in arbitrary $C^{4,\gamma}$-smooth domains.Maximum principles do not exist for fourth order elliptic equations and theGreen function may change sign. It prevents using a Harnack inequality as forsecond order problems and hence complicates the derivation of optimalestimates. The present estimate is obtained by an asymptotic analysis. Theestimate shows that this Green function is positive near the singularity andthat a possible negative part is small in the sense that it is bounded by theproduct of the squared distances to the boundary.

Optimal estimates from below for biharmonic Green functions