Carleman’s formulas for the Laplace and Poisson equations with operator coefficients
Eduard Vitalievich Arbuzov, A. L. Bukhgeĭm · Journal of Inverse and Ill-Posed Problems · 2001
Abstract - The Cauchy problems for operator analogues of the Laplace and Poisson equations with data known on a part of the domain boundary are considered. For solutions of these problems formulas of Carleman type are derived. The formulas obtained can be used in investigation of two-dimensional tomography problems with incomplete data.