|
Abstract |
I first survey results on gradient estimates for solutions and determination of inclusion to divergence form elliptic equations and systems with discontinuous principal coefficients. Then I will present some recent work with my colleagues on gradient estimates of solutions of Lame systems with partial infinity coefficients, and give optimal blow up rate of the gradient of solutions as the distance between the surfaces of discontinuity of the coefficients. Finally we concern the infinitely rigid inclusions in linear elasticity, and establish the necessary and sufficient conditions for “the inclusion is an ellipsoid in an infinite media” under any uniform applied loading, which are related to Eshelby conjecture. |
