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The Dirichlet problem in Lipschitz domains with boundary data in Besov spaces for higher order elliptic systems with rough coefficients

Research paper by Vladimir Maz'ya, Marius Mitrea, Tatyana Shaposhnikova

Indexed on: 09 Jun '05Published on: 09 Jun '05Published in: Mathematics - Analysis of PDEs



Abstract

We settle the issue of well-posedness for the Dirichlet problem for a higher order elliptic system ${\mathcal L}(x,D_x)$ with complex-valued, bounded, measurable coefficients in a Lipschitz domain $\Omega$, with boundary data in Besov spaces. The main hypothesis under which our principal result is established is in the nature of best possible and requires that, at small scales, the mean oscillations of the unit normal to $\partial\Omega$ and of the coefficients of the differential operator ${\mathcal L}(x,D_x)$ are not too large.