A Bilinear Estimate for Biharmonic Functions in Lipschitz Domains
نویسندگان
چکیده
We show that a bilinear estimate for biharmonic functions in a Lipschitz domain Ω is equivalent to the solvability of the Dirichlet problem for the biharmonic equation in Ω. As a result, we prove that for any given bounded Lipschitz domain Ω in Rd and 1 < q < ∞, the solvability of the Lq Dirichlet problem for ∆2u = 0 in Ω with boundary data in WA(∂Ω) is equivalent to that of the Lp regularity problem for ∆2u = 0 in Ω with boundary data in WA(∂Ω), where 1p + 1 q = 1. This duality relation, together with known results on the Dirichlet problem, allows us to solve the Lp regularity problem for d ≥ 4 and p in certain ranges. MSC (2000): 35J40.
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