Sharp trace regularity for an anisotropic elasticity system

Sharp trace regularity for an anisotropic elasticity system

In this paper, we establish an optimal trace regularity theorem, also known as the hidden regularity theorem [L2], for the anisotropic linear elasticity equation on a bounded domain Ω with Lipschitz boundary. In its simplest form it provides a space-time L estimate for the trace of the normal derivative for the solution. Over the years, such sharp trace regularity theorems have proven to be cru...

Sharp Trace Regularity for the Solutions of the Equations of Dynamic Elasticity

Sharp trace regularity results have proven themselves to be of critical importance in the study of controllability and stabilizability of various systems, as well as being of great interest in their own right. Particular cases include the wave equation (see [9]) and both linear and nonlinear plate equations (see [5], [8]). In our study of the three-dimensional system of linear elasticity, we fo...

Regularity under Sharp Anisotropic General Growth Conditions

We prove boundedness of minimizers of energy-functionals, for instance of the anisotropic type (1.1) below, under sharp assumptions on the exponents pi in terms of p ∗: the Sobolev conjugate exponent of p; i.e., p∗ = np n−p , 1 p = 1 n Pn i=1 1 pi . As a consequence, by mean of regularity results due to Lieberman [21], we obtain the local Lipschitz-continuity of minimizers under sharp assumptio...

Sharp Trace Regularity for the Solutions of theEquations of Dynamic

An alternative to the Kelvin decomposition for plane anisotropic elasticity