This monograph is devoted to a study of certain Hardy-type inequalities for non-convex domains in R^n. For convex domains, 1/4 is the precise value of the constant in such inequalities. This book is concerned with finding estimates on that constant for non-convex multi-dimensional domains. Some estimates were obtained earlier by other authors for simply connected planar domains with the help of complex-analytic methods. Our aim is to obtain lower bounds for the optimal constant by real-analytic methods.