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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.