Mappings of finite distortion: Monotonicity and continuity

By Tadeusz Iwaniec, Pekka Koskela, Jani Onninen. 2001

240 citations recorded by the source corpus.

Subfields: Computational Mechanics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/fb4f1385d7b7443a9664db1a3a1123329dbdaf6e

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In Computational Mechanics

In Geometry and Topology

Citations in the corpus

Mappings of finite distortion: Sharp Orlicz-conditions (2003, methodology): “1 were established in [6], [9] and [10] for Ψ(t) = λt, λ > 0.”
A Note on the Boundedness of the Hilbert Transform in Weighted Grand Lebesgue Spaces (2009, methodology): “For some properties and applications of L spaces we refer to the papers [5], [7], [2], [1].”
Mappings of Finite Distortion:¶Discreteness and Openness (2001, background): “This paper is a crucial part of our program to establish the fundamentals of the theory of mappings of finite distortion [11,1,12,17] which form a natural generalization of the class of quasiregular mappings, also called mappings of bounded distortion.”
Structural properties of Bilateral Grand Lebesque Spaces (2010, methodology): “, for random variables are used in PDE [5]–[8], probability in Banach spaces [14], in the modern non-parametrical statistics, for example, in the so-called regression problem [15, 16].”
Mappings of finite distortion: Capacity and modulus inequalities (2006, background): “Mappings like this are called mappings of finite distortion in [8], [12], [14].”
The maximal theorem for weighted grand Lebesgue spaces (2008, background): “[7], [9], [2] and references therein), which are rearrangement-invariant Banach function spaces (see e.”
On grand and small Lebesgue and Sobolev spaces and some applications to PDE's (2018, background): “The interested reader can see the papers [18, 87, 94, 23].”
Hyperelastic Deformations of Smallest Total Energy (2009, background): “onto −→ Y of finite distortion [ 29 ,37,38]. While in this article we have little to do with the advanced aspects of nonlinear elasticity, adopting its general ideas is almost indispensable.”
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].”
Mappings of finite distortion: The zero set of the Jacobian (2003, background): “By the results in [10], [15] and [17], f is continuous and both open and discrete.”