This monograph presents a rigorous mathematical framework for a linear
elastic model arising from volcanology that explains deformation effects
generated by inflating or deflating magma chambers in the Earth's
interior. From a mathematical perspective, these modeling assumptions
manifest as a boundary value problem that has long been known by
researchers in volcanology, but has not, until now, been given a
thorough mathematical treatment. This mathematical study gives an
explicit formula for the solution of the boundary value problem which
generalizes the few well-known, explicit solutions found in geophysics
literature. Using two distinct analytical approaches-one involving
weighted Sobolev spaces, and the other using single and double layer
potentials-the well-posedness of the elastic model is proven. An
Elastic Model for Volcanology will be of particular interest to
mathematicians researching inverse problems, as well as geophysicists
studying volcanology.