Symmetrization in Anisotropic Elliptic Problems

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Uniqueness (2021, unknown): “4), we show that the solutions are essentially bounded via modern, general versions of Talenti’s rearrangement argument [12] and De Giorgi’s technique [2] (vide Lemmas 4.”
Fully anisotropic elliptic problems with minimally integrable data (2019, unknown): “Φ(Ω), (ii) the family {εAe(A′(|∇uε|))} is uniformly bounded in L1(Ω), (iii) the family {a(x,∇uε)} is uniformly bounded in LΦe(Ω;Rn). Proof. We shall make use of a comparison principle estanblished in [Ci5], that links the solution uε to the solution vto the symmetrized problem (6.14) −div Φ♦(|∇v”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, methodology): “It has been developed in PDE context in [52, 55] and applied in studies on existence and regularity [9, 15, 14, 10, 11, 18].”