An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs

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On $$C^1$$C1, $$C^2$$C2, and weak type-(1, 1) estimates for linear elliptic operators: part II (2017, methodology): “14 is in the spirit of Campanato’s method [4] as presented in a modern textbook [13].”
A higher-order large-scale regularity theory for random elliptic operators (2015, background): “1 in [9]), there exists a bounded, symmetric, and uniformly elliptic coefficient field a0 which is radial and smooth away from the origin, for which the map u0(x) := x |x|γ (53) with γ := 32 (1 − 1 √ 17 ) is a0-harmonic.”
Boundary regularity via Uhlenbeck–Rivière decomposition (2008, unknown): “2) 6Here we use ‖g‖ W 1,p 0 ≤ C‖4g‖ (W 1,p 0 ) ∗ which is true for p ≥ 2 (see for example [GM05], Theorem 7.”
Interior regularity of solutions of non-local equations in Sobolev and Nikol’skii spaces (2016, methodology): “Nice presentations of this technique are for instance contained in [E98] and [GM12].”
John–Nirenberg lemmas for a doubling measure (2009, background): “The original proof in [11], based on an induction argument, can be found with more details in [8] and [7].”