Symmetry for exterior elliptic problems and two conjectures in potential theory

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Symmetry results for viscosity solutions of fully nonlinear uniformly elliptic equations (2007, background): “1, and, in a similar manner, that the arguments from [23] can be used to prove Theorems 1.”
Characterization of balls by Riesz-potentials (2009, background): “[6] and the higher-dimensional case by Reichel [17], Mendez and Reichel [14] and Sirakov [19].”
Solutions to overdetermined elliptic problems in nontrivial exterior domains (2016, unknown): “This last result in [19] is still true if we replace the Laplacian operator ∆ by a regular strongly elliptic operator, as shown by Sirakov in [27].”
Overdetermined problems with fractional Laplacian (2013, background): “Since a complete list of references cannot be given, we only quote: [1, 4, 7, 8, 11, 10, 12, 19, 20, 22, 23, 25, 28, 31, 32, 34, 33, 39, 38].”
Partially overdetermined elliptic boundary value problems (2008, background): “In this case it is known that, whenever a solution exists, necessarily Ω is a ball (see [14,32,35]).”