Hardy Inequalities and Applications: Inequalities with Double Singular Weight

This book derives new Hardy inequalities with double singular weights - at an interior point and on the boundary of the domain. We focus on the optimality of Hardy constant and on its attainability. Applications include: results about existence\nonexistence and controllability for parabolic equations with double singular potentials; estimates from below of the fi rst eigenvalue of p-Laplacian with Dirichlet boundary conditions.