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In this paper, we prove two unique continuation results for second orderelliptic equations with Robin boundary conditions on $C^{1,1}$ domains. Thefirst one is a sharp vanishing order estimate of Robin problems with Lipschitzcoefficients and differentiable, sign-changing potentials. This generalizes theresult for the "Robin eigenfunctions" in [26], which deals with the case withconstant potentials. The second result is a unique continuation result from theboundary -- any non-trivial solution cannot vanish at infinite order from theboundary or vanish on an open subset on the boundary. Such result generalizesthe one in [1] for the Laplace equation on $C^{1,1}$ domains with zero Neumannboundary conditions.

Quantitative unique continuation for Robin boundary value problems on $C^{1,1}$ domains