Solvability of the three-dimensional thermistor problem

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On variational problems and nonlinear elliptic equations with nonstandard growth conditions (2011, background): “The solvability of the threedimensional problem (17.1) is established in [ 71 ] on the basis of a rather complicated derivation of an estimate of the form (1.20).”
Monotone operator theory for unsteady problems in variable exponent spaces (2012, background): “A similar energy also appears in Zhikov’s model for the thermistor problem in [7], or in the investigation of variational integrals with non-standard growth by Acerbi and Mingione in [8–10].”
Regularity of solutions to a class of variable–exponent fully nonlinear elliptic equations (2018, background): “For completeness, we mention that variational exponents appear also in the context of electrorheological fluids [29, 31, 32] and the thermistor problem [41]; see also [6] and the references therein.”