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A monotonicity approach to the study of the asymptotic behavior near cornersof solutions to semilinear elliptic equations in domains with a conicalboundary point is discussed. The presence of logarithms in the first term ofthe asymptotic expansion is excluded for boundary profiles sufficiently closeto straight conical surfaces.

Almgren-type monotonicity methods for the classification of behavior at corners of solutions to semilinear elliptic equations