Geometric Function Theory and Non-linear Analysis

By Tadeusz Iwaniec, Gaven J. Martin. 2002

762 citations recorded by the source corpus.

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Citations in the corpus

Existence of energy-minimal diffeomorphisms between doubly connected domains (2010, background): “2)|2 6 C R 2D|Df| 2 log e+ diamD |z1−z2| , EXISTENCE OF ENERGY-MINIMAL DIFFEOMORPHISMS 7 with z1,z2 ∈ Dfor a pair of concentric disks D⊂ 2D⊂ U. The constant C is universal. See, e.g., Corollary 7.5.1 [19]. Theoscillation property (3.1) obviously holdsfor all homeomorphismsand is preserved under c-un”
n-Harmonic Mappings Between Annuli (2011, methodology): “We shall employ the operator norm of the differential matrix, commonly used in the literature [29, 43, 44].”
On the theory of mappings with finite area distortion (2008, unknown): “[AIKM], [GI], [HK], [IKO1], [IKO2], [ IM ], [IR], [IS], [KKM1], [KKM2], [KO], [MRSY1], [MRSY2], [MV1], [MV2], [RSY1] - [RSY3].”
The foundational inequalities of D.L. Burkholder and some of their ramifications (2010, background): “of conformally invariant energy functionals and regularity of solutions to the generalized Beltrami system, see [7, 98, 99].”
Form boundedness of the general second‐order differential Operator (2004, unknown): “, [IM]) : 〈DivF, ~v〉 = −trace 〈F , D~v〉, ~v ∈ C∞ 0 (R), where F t = (fji) n i,j=1 is the transposed matrix field.”
Equicontinuity of mappings quasiconformal in the mean (2010, background): “related references in the monographs [9] and [17].”
A note on extremal mappings of finite distortion (2005, unknown): “This together with (7) and (18) implies that ||Dh(y) || 2 ≤ CK (h(y), f)J(y, h) a.”
Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A (2015, background): “For a discussion of this result (including the definition of linear Lebesgue measure zero), see the discussion of “Painlevé’s theorem” in Iwaniec–Martin [279] or see Pajot [424].”
Mappings of finite distortion: Capacity and modulus inequalities (2006, background): “something slightly weaker, cf. [ 10 ]) suffices in all dimensions.”
Harmonic type approximation lemmas (2009, background): “p-Harmonic maps are of fundamental importance today, both in applied pde, where they serve to give a model for pdes describing several physical phenomena, especially in the evolutionary case [19,5], and for instance in modern geometric analysis, due to their natural connection with quasiconformal ma”
On grand and small Lebesgue and Sobolev spaces and some applications to PDE's (2018, unknown): “[95]): ‖ f‖Lnp/(n−p)(Bn) p(n−1) n− p ‖∇ f‖Lp(Bn) ∀ f ∈W 1,p 0 (Bn), ∀n > p”
KLEINIAN GROUPS IN HIGHER DIMENSIONS (2007, unknown): “We refer the reader to [94, 99] for the definitions of quasisymmetric and quasiconformal homeomorphisms.”
Geometric Group Theory (2018, methodology): “35 (Tukia’s Strong Convergence Property, [Tuk86]; see also [IM01] for a stronger version).”
Invariant distributions, Beurling transforms and tensor tomography in higher dimensions (2014, background): “Related transforms have been studied on differential forms in Rn [27], on Riemannian manifolds [34], and in hyperbolic space [25].”