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This book focuses on the mathematical potential and computational efficiency of the Boundary Element Method (BEM) for modeling seismic wave propagation in either continuous or discrete inhomogeneous elastic/viscoelastic, isotropic/anisotropic media containing multiple cavities, cracks, inclusions and surface topography.

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 the sharpness of Hardy inequality. Applications include: results about existence
onexistence and controllability for parabolic equations with double singular potentials; estimates from below of the first eigenvalue of p-Laplacian with Dirichlet boundary conditions.