In this paper, we investigate divergence-form linear elliptic systems on bounded Lipschitz domains in ℝ d + 1 , d≥ 2 , with L 2 boundary data. The coefficients are assumed to be real, bounded, and measurable. We show that when the coefficients are small, in Carleson norm, compared to one that is continuous on the boundary, we obtain solvability for both the Dirichlet and regularity boundary value problems given that the coefficients satisfy a certain “pseudo-symmetry” condition.
- Bounded Lipschitz domains
- Linear elliptic systems
- Second order
- Small Carleson norm condition
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