Sign-Preserving Property for Some Fourth-Order Elliptic Operators in One Dimension and Radial Symmetry

Philippe Laurencot (1) , Christoph Walker (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IFAM - Institut für Angewandte Mathematik

For a class of one-dimensional linear elliptic fourth-order equations with homogeneous Dirichlet boundary conditions it is shown that a non-positive and non-vanishing right-hand side gives rise to a negative solution. A similar result is obtained for the same class of equations for radially symmetric solutions in a ball or in an annulus. Several applications are given, including applications to nonlinear equations and eigenvalue problems.

Mots clés: Maximum principle; fourth-order equations; MEMS

Domaines: Equations aux dérivées partielles [math.AP]

Philippe Laurencot, Christoph Walker. Sign-Preserving Property for Some Fourth-Order Elliptic Operators in One Dimension and Radial Symmetry. Journal d'analyse mathématique, 2015, 127, pp.69--89. ⟨hal-00798584⟩