INTEGRABILITY-PRESERVING REGULARIZATIONS OF LAPLACIAN GROWTH

The paper’s Section 3.3 defines the weak Laplacian Growth boundary as the zero set of ∂zΨ and explicitly notes that for classical times the boundary satisfies V′(z)+C_{μt}(z)=0, so that the gradient of Ψ vanishes exactly on ∂Ω(t) . It also states that weak solutions built from equilibrium measures persist beyond the critical time and are monotone in the sense K(s)⊆K(t), supp μ(s)⊆supp μ(t) , and remarks that on supp μt the tangential derivative of Ψ vanishes while the two normal limits are equal and opposite, cohering with the S-property picture used by the model solution . The candidate solution recovers these conclusions via potential-theoretic Euler–Lagrange/S-property methods and Gustafsson’s variational-inequality framework. It further adds standard details (meromorphic extension of Q² and quadratic differential trajectories) that the paper alludes to via branch-point/Riemann-surface data but does not spell out. Hence both are correct; the paper sketches the construction while the model provides a more detailed potential-theoretic route.