• Media type: E-Article
  • Title: Certain Estimates for Solutions of Nonlinear Elliptic Differential Equations Applicable to the Theory of Thin Plates
  • Contributor: Komkov, V.
  • Published: Society for Industrial and Applied Mathematics, 1975
  • Published in: SIAM Journal on Applied Mathematics, 28 (1975) 1, Seite 24-34
  • Language: English
  • ISSN: 0036-1399
  • Origination:
  • Footnote:
  • Description: This article derives certain estimates based on properties of the Lagrangian integral for (classical) solutions of equations of the form \begin{equation*}\tag{(1)}\sum_i(a_i(x)\phi(w)w_{x_i})_{x_i} + c( \mathbf{x})f(w) = 0,\end{equation*} and \begin{equation*}\tag{(2)}\sum_j \sum_i(a_i(\mathbf{x})\phi(w)w_{x_ix_i})_{x_jx_j} + c(\mathbf{x})f(w) = 0,\end{equation*}$x \in \Omega \subset \mathbb{R}^n$, where ai(x) are positive in Ω. These estimates depend on the size and shape of Ω, but do not depend on the boundary conditions imposed on ∂Ω. Examples are given of applications to nonlinear membrane and both linear and nonlinear thin plate theory.