Some Phragmén-Lindelöf type results for the biharmonic equation
Eliminating a priori decay assumptions of Phragmén-Lindelöf type, growth-decay estimates for some weighted and unweighted energy expressions are derived. Three special types of unbounded domains (so- called semi-infinite strips of variable thickness) in \(\mathbb{R}^ 2\) with Dirichlet type boundary conditions are considered. The derivations are based on the application of the Wirtinger and Schwarz inequalities. The basic inequality which is used to prove the energy estimates is \[ |\varphi (z)|\leq (h^ 2/2\pi) \varphi''(z). \] Explicit bounds are also given for the total energy. The end of the paper outlines how the obtained results for 2D may be extended to analogous problems in \(\mathbb{R}^ 3\).
scientific article; zbMATH DE number 636031