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New completeness theorems on the boundary in Elasticity

Alberto Cialdea

Abstract

The completeness on the boundary (in the sense of Picone) of certain systems related to the III and IV BVPs for the elasticity system is proved. The completeness is obtained in both $L^p$ ($1\leq 1<\infty$) and uniform norms.

New completeness theorems on the boundary in Elasticity

Abstract

The completeness on the boundary (in the sense of Picone) of certain systems related to the III and IV BVPs for the elasticity system is proved. The completeness is obtained in both () and uniform norms.
Paper Structure (6 sections, 24 theorems, 127 equations)

This paper contains 6 sections, 24 theorems, 127 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The class $\mathop{\mathscr A}\nolimits^p(\Omega)$
  4. Polynomial solutions
  5. Completeness Theorems in $L^p$ norm
  6. Completeness in the uniform norm

Key Result

Theorem 1

If $\Sigma$ is not an axially symmetrical surface, then for any given $(\varphi, \Phi)\in C^{1,\beta}(\Sigma)\times [C^{\beta}(\Sigma)]^{3}_{0}$ problem eq:BVPIII has a unique regular solution. If $\Sigma$ is an axially symmetrical surface different from a sphere, then, given $(\varphi, \Phi)\in C^{ where $a$ is the unit vector of the rotation axis and $x^0$ is an arbitrary point on this axis, the

Theorems & Definitions (26)

  • Theorem 1
  • Theorem 2
  • Remark 1
  • Remark 2
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Theorem 6
  • Theorem 7
  • Theorem 8
  • ...and 16 more