Hardy-type inequalities with sharp constants in domains lambda-close to convex (Q2671971)

In this paper, the author studies the Hardy-type inequalities for real-valued functions vanishing on the boundary of a domain of Euclidean space under the assumption that the domain is lambda-close to convex and obtains some new integral inequalities with sharp constants. Furthermore, using the inner products of the gradients of the distance function from a point to the boundary of the domain by test functions, both the standard and strengthen Hardy-type inequalities are derived and discussed.