Abstract
Letφ, ψ be smooth functions on the boundary of the unit diskB 1. A second order uniformly elliptic operatorL and a functionu with second order derivatives inL p (1<p<2) are constructed with the following properties:u solvesLu=0 inB 1 and satisfies the Cauchy dataφ, ψ on∂B 1.
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Cavazzoni, R. On the Cauchy problem for elliptic equations in a disk. Rend. Circ. Mat. Palermo 52, 131–140 (2003). https://doi.org/10.1007/BF02871927
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DOI: https://doi.org/10.1007/BF02871927