A monotonicity approach to the study of the asymptotic behaviour near corners of solutions to semilinear elliptic equations in domains with a conical boundary point is discussed. The presence of logarithms in the first term of the asymptotic expansion is excluded for boundary profiles sufficiently close to straight conical surfaces.
Felli, V., Ferrero, A. (2013). Almgren-type monotonicity methods for the classification of behaviour at corners of solutions to semilinear elliptic equations. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS, 143(5), 957-1019 [10.1017/S0308210511001314].
Almgren-type monotonicity methods for the classification of behaviour at corners of solutions to semilinear elliptic equations
FELLI, VERONICA;
2013
Abstract
A monotonicity approach to the study of the asymptotic behaviour near corners of solutions to semilinear elliptic equations in domains with a conical boundary point is discussed. The presence of logarithms in the first term of the asymptotic expansion is excluded for boundary profiles sufficiently close to straight conical surfaces.
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