Wiener Type Regularity of a Boundary Point for the 3D Lam\'e System

TL;DR

This paper investigates the Wiener regularity of boundary points for the 3D Lamé system, establishing conditions under which solutions are continuous at boundary points based on weighted positive definiteness and Wiener integral divergence.

Contribution

It extends the theory of Wiener regularity to the 3D Lamé system by linking weighted positive definiteness with boundary solution continuity.

Findings

Weighted positive definiteness holds for certain elastic constants.

Divergence of Wiener integral implies boundary solution continuity.

Modified theory from Maz'ya (2002) applies to Lamé system.

Abstract

In this paper, we study the 3D Lam\'e system and establish its weighted positive definiteness for a certain range of elastic constants. By modifying the general theory developed in Maz'ya (2002), we then show, under the assumption of weighted positive definiteness, that the divergence of the classical Wiener integral for a boundary point guarantees the continuity of solutions to the Lam\'e system at this point.