A note on a weakly singular elliptic equation from theory of elasticity

TL;DR

This paper investigates the qualitative behavior of solutions to a second order elliptic equation from anisotropic elasticity, including explicit solutions for disks and analysis of singularities at the origin.

Contribution

It provides explicit solutions for a disk and analyzes how solution behavior depends on coefficients, addressing singularities at the origin.

Findings

Explicit solutions for a disk are derived.

Solution behavior varies with coefficients.

Singularities at the origin are discussed.

Abstract

Qualitative properties of a second order elliptic equation from the anisotropic elasticity are investigated. Some explicit solutions for a disk are presented. Behaviour of these solutions in dependence of coefficients is investigated. The problem of presence of singularities of solutions at the origin of coordinates is discussed.