Behavior of the gradient of the solution of the Dirichlet problem for the biharmonic equation near a boundary point of a three-dimensional domain (Q804754)

The relative capacity \(\Gamma\) (e,G) of a compact e, \(e\subset G\), where G is an open bounded set from \({\mathbb{R}}^ 3\), is introduced and several properties of it are studied. There are also described some integral formulas relative to a class of functions with compact support defined on an open relatively compact set. All these results are applied to the study of the solutions of the Dirichlet problem for the biharmonic equation near a boundary point of a three-dimensional domain. the main result describes an upper bound for an integral which depends on a solution of the Dirichlet problem. The authors carefully discuss some relevant examples.