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• W2103227219 abstract "We study the homogeneous elliptic systems of order $$2ell$$ with real constant coefficients on Lipschitz domains in $$mathbb{R}^n$$ , $$nge 4$$ . For any fixed p > 2, we show that a reverse Hölder condition with exponent p is necessary and sufficient for the solvability of the Dirichlet problem with boundary data in L p . We also obtain a simple sufficient condition. As a consequence, we establish the solvability of the L p Dirichlet problem for $$nge 4$$ and $$2-epsilon< p<frac{2(n-1)}{n-3} +epsilon$$ . The range of p is known to be sharp if $$ellge 2$$ and $$4le nle 2ell + 1$$ . For the polyharmonic equation, the sharp range of p is also found in the case n = 6, 7 if $$ell=2$$ , and $$n=2ell+2$$ if $$ellge 3$$ ." @default.
• W2103227219 created "2016-06-24" @default.
• W2103227219 creator A5065781968 @default.
• W2103227219 date "2006-06-29" @default.
• W2103227219 modified "2023-10-15" @default.
• W2103227219 title "Necessary and Sufficient Conditions for the Solvability of the L p Dirichlet Problem on Lipschitz Domains" @default.
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• W2103227219 doi "https://doi.org/10.1007/s00208-006-0022-x" @default.
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