Determining the temperature from Cauchy data in corner domains
The paper is concerned with the analysis of the solvability of the problem to reconstruct the temperature in a plane domain containing corner points from the knowledge of the temperature and heat flux only on a portion of the boundary. The model is based on the classical linear heat equation with a smooth thermal coefficient. The solution procedure is an iterative scheme involving two mixed problems, one obtained from the original equations with the substitution of the Newman condition with a Dirichlet condition on the remaining part of the boundary, the other is its adjoint. The main result is the proof of solvability of the mixed problem in a weighted Sobolev space. The choice of the space is determined by the presence of singularity due to the corners and the mixed type of boundary conditions. The result generalizes the time depended case of a previous paper of the same author [\textit{T. Johansson} and \textit{L. Marin}, Inverse Probl. 23, No. 1, 357--372 (2007; Zbl 1119.35114)].
scientific article; zbMATH DE number 5771947