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

TL;DR

This paper develops Almgren-type monotonicity methods to analyze the behavior of solutions to semilinear elliptic equations near corners, showing that logarithmic terms are absent in asymptotic expansions for certain boundary profiles.

Contribution

It introduces a monotonicity approach to classify solution behavior at corners, excluding logarithmic terms for near-straight conical boundary profiles.

Findings

Logarithmic terms are excluded in asymptotic expansions near corners.

The method applies to solutions with boundary profiles close to straight cones.

Provides a new classification framework for corner behaviors in elliptic equations.

Abstract

A monotonicity approach to the study of the asymptotic behavior 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.