Sharp trace regularity for an anisotropic elasticity system
نویسندگان
چکیده
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 crucial for obtaining well-posedness, controllability and boundary stabilization results for a variety of hyperbolic and partially hyperbolic systems, [LTr1, LTr2, LT, BL, LTu]. For the wave equation, the analog of the result proved in this work for the anisotropic elasticity equation (see [L2]), was an essential ingredient in deriving a well-posedness theorem for a fluid-structure
منابع مشابه
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...
متن کاملShanks Workshop on Mathematical Aspects of Fluid Dynamics
In this talk, I will describe the simplified version of Ericksen and Leslie that models the hydrodynamic flow of nematic liquid crystals, which is a governing equation for the macroscopic continuum description of evolution of the material under the influence of both fluid velocity field and the macroscopic average of the microscopic orientation of rod-like liquid crystal molecules. I will indic...
متن کاملControl-theoretic Properties of Structural Acoustic Models with Thermal Effects, Ii. Trace Regularity Results
We consider a structural acoustic problem with the flexible wall modeled by a thermoelastic plate, subject to Dirichlet boundary control in the thermal component. We establish sharp regularity results for the traces of the thermal variable on the boundary, in the case the system is supplemented with clamped mechanical boundary conditions. These regularity estimates are most crucial for validity...
متن کاملRegularity 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...
متن کاملAnisotropic Regularity and Optimal Rates of Convergence for the Finite Element Method on Three Dimensional Polyhedral Domains
We consider the model Poisson problem −∆u = f ∈ Ω, u = g on ∂Ω, where Ω is a bounded polyhedral domain in Rn. The objective of the paper is twofold. The first objective is to review the well posedness and the regularity of our model problem using appropriate weighted spaces for the data and the solution. We use these results to derive the domain of the Laplace operator with zero boundary condit...
متن کامل