Abstract
LetC be a curve which is conformal to a pair of line segments meeting at an angle α strictly between 0 and π,u a biharmonic function analytic in a neighbourhood ofC, whose gradient vanishes onC. It is shown thatu(x, y) must be constant.
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Boyling, J.B. A rigidity result for biharmonic functions clamped at a corner. Z. angew. Math. Phys. 46, 289–294 (1995). https://doi.org/10.1007/BF00944759
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DOI: https://doi.org/10.1007/BF00944759