Optimal boundary gradient estimates for Lam\'{e} systems with partially infinite coefficients

TL;DR

This paper establishes optimal gradient estimates for solutions to Lamé systems with partially infinite coefficients near boundary discontinuities, revealing blow-up rates as inclusions approach the boundary in various dimensions.

Contribution

It provides the first precise boundary gradient bounds and blow-up rates for Lamé systems with partially infinite coefficients near boundary discontinuities.

Findings

Optimal gradient bounds derived for Lamé systems

Blow-up rates established as inclusions approach the boundary

Results hold for arbitrary shapes and all dimensions

Abstract

In this paper, we derive the pointwise upper bounds and lower bounds on the gradients of solutions to the Lam\'{e} systems with partially infinite coefficients as the surface of discontinuity of the coefficients of the system is located very close to the boundary. When the distance tends to zero, the optimal blow-up rates of the gradients are established for inclusions with arbitrary shapes and in all dimensions.