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

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

2005-05-18

arxiv.org/abs/math/0505372v3

Mathematics

Analysis of PDEs

54 pages

Scientific paper

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.

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