BMO AND LIPSCHITZ APPROXIMATION BY SOLUTIONS OF ELLIPTIC-EQUATIONS

We consider the problem of qualitative approximation by solutions of a constant coefficients homogeneous elliptic equation in the Lipschitz and BMO norms. Our method of proof is well-known : we find a sufficien t condition for the approximation reducing matters to a weak spectra l synthesis problem in an appropriate Lizorkin-Triebel space. A couple of examples, evolving from one due to Hedberg, show that our conditio ns are sharp.