Solutions of Semilinear Elliptic Equations in with Conical&Shaped Level Sets

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Asymptotic properties and classification of bistable fronts with Lipschitz level sets (2005, background): “4 in [10] can then be applied to u = v and u = u.”
Existence and qualitative properties of multidimensional conical bistable fronts (2005, background): “For every λ ∈ (0, 1) the function u satisfies (1.10) lim sup A→+∞, y≥A+φλ(x) |u(x, y)− 1| = 0, lim sup A→−∞, y≤A+φλ(x) |u(x, y)| = 0 Furthermore, all functions φλ have the same Lipschitz norm, say cotα with α ∈ (0, π/2], x̂ · ∇φλ(x) → − cotα as |x| → +∞, and c = c0/ sinα.”
Front propagation in periodic excitable media (2002, methodology): “We use here a method similar to that of Li [73] or Vega [97] for strictly elliptic problems (see other applications of this method in [48]).”