Removable singularities in the boundary for quasilinear elliptic equations

TL;DR

This paper investigates conditions under which boundary singularities in quasilinear elliptic equations can be removed, using asymptotic analysis and Sobolev norm conditions to characterize their removability.

Contribution

It introduces two novel approaches—via asymptotic behavior and Sobolev norms—to determine boundary singularity removability in quasilinear elliptic equations.

Findings

Characterizes boundary singularity removability using asymptotic behavior.

Establishes conditions based on Sobolev norms for singularity removability.

Provides criteria applicable to various classes of quasilinear elliptic equations.

Abstract

In this work, we are interested in to study removability of a singular set in the boundary for some classes of quasilinear elliptic equations. We will approach this question in two different ways: through an asymptotic behavior at the infinity of the solutions, or through conditions in the Sobolev norm of solutions along the direction of the singular set.