ON THE DEPENDENCE OF SOLUTIONS OF BOUNDARY VALUE PROBLEMS ON PERTURBATION OF THE DOMAIN BY VECTOR FIELDS

Regular dependence theorems are presented and growth estimates in H?lder norms are established for the solutions of boundary value problems, under perturbation of the domain by vector fields. The question of parametrization of domains is considered. The results obtained are applied to the analysis of operator functions which arise in the study of a free boundary problem.