On the structure of biharmonic functions satisfying the clamped plate conditions on a right angle |
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Authors: | C V Coffman R J Duffin |
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Institution: | Department of Mathematics, Camegie-Mellon University, Pittsburgh, Pennsylvania 15213 U.S.A. |
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Abstract: | Let u(r,θ) be biharmonic and bounded in the circular sector ¦θ¦ < π/4, 0 < r < ρ (ρ > 1) and vanish together with δu/δθ when ¦θ¦ = π/4. We consider the transform û(p,θ) = ∝01rp − 1u(r,θ)dr. We show that for any fixed θ0 u(p,θ0) is meromorphic with no real poles and cannot be entire unless u(r, θ0) ≡ 0. It follows then from a theorem of Doetsch that u(r, θ0) either vanishes identically or oscillates as r → 0. |
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