A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation

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A quasi-reversibility approach to solve the inverse obstacle problem (2010, methodology): “The proof of proposition 6 is very similar to the proofs provided in [1, 2] in slightly different cases, this is why it is not reproduced here.”
A Highly Accurate MCTM for Inverse Cauchy Problems of Laplace Equation in Arbitrary Plane Domains (2008, background): “…of this type problems, e.g., Andrieux, Baranger and Ben Abda (2006), Aparicio and Pidcock (1996), Ben Belgacem and El Fekih (2005), Berntsson and Eldén (2001), Bourgeois (2005, 2006); Chapko and Kress (2005), Kress (2004), Mera, Elliott, Ingham and Lesnic (2000), and Slodicka and Van Keer (2004).”
Solving Cauchy problems by minimizing an energy-like functional (2006, methodology): “Various algorithms have been proposed including the least-squares method [16], moment methods [5], optimal control techniques [30] or quasireversibility methods [ 12 , 28].”