Renormalized solutions for nonlinear elliptic equations with variable exponents and L1 data

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Overview of differential equations with non-standard growth (2010, background): “These are not further discussed here, but see [48] for recent results in the variable exponent case.”
Renormalized solutions of nonlinear elliptic problems in generalized Orlicz spaces (2012, background): “For results on existence of renormalized solutions of elliptic problems of type (E, f) with a(·, ·) satisfying a variable growth condition we refer to [20], [43] (for related results see also [9], [10], [42]).”