In the first part of the seminar I will present a physical model used in volcanology to describe ground's deformations within calderas. Based on the linear elastic theory, this analytical model replaces caldera with a half-space and the magma chamber by a pressurized cavity of small dimensions compared to its depth. Using these hyphoteses, in the second part of the talk, I will consider the scalar version of this model concerning the Laplace equation with Neumann boundary conditions on the half-space and the cavity. I will exhibit some results on the well-posedness of this problem and then the asymptotic formula for the solution within the framework of layer potentials techniques. This is a joint work with Elena Beretta and Corrado Mascia.