Convergence rates for the quasi-reversibility method to solve the Cauchy problem for Laplace's equation

We consider the quasi-reversibility method to solve the Cauchy problem for Laplace's equation in a smooth bounded domain. We assume that the Cauchy data are contaminated by some noise of amplitude σ, so that we make a regular choice of ε as a function of σ, where ε is the small parameter of the quasi-reversibility method. Specifically, we present two different results concerning the convergence rate of the solution of quasi-reversibility to the exact solution when σ tends to 0. The first result is a convergence rate of type in a truncated domain, the second one holds when a source condition is assumed and is a convergence rate of type in the whole domain.