Anisotropic Sobolev homeomorphisms

Gironimo, Patrizia Di; D'Onofrio, Luigi; Sbordone, Carlo; Schiattarella, Roberta

doi:10.5186/aasfm.2011.3632

Cited by 18 publications

(6 citation statements)

References 18 publications

(20 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our technique are completely different; in fact we slice homeomorphism along coordinate directions. Theorem 1.7 generalizes the result of [4].…”

supporting

confidence: 51%

“….0; 1/ is the usual Cantor ternary function, is a Lipschitz homeomorphism whose inverse f 1 0 does not belong to W 1;1 loc , it is only of bounded variation. However, for this kind of mappings analogous identities have been recently found in [4].…”

Section: Introductionmentioning

confidence: 87%

“…The statement of Theorem 1.3 is actually contained in [4] with the additional assumption for mappings f 2 W 1;1 loc . However, with some technical tools given here (see Section 3), it is possible to prove identities for the wider class of mappings with bounded variation.…”

mentioning

confidence: 98%

See 2 more Smart Citations

On the total variations for the inverse of a BV-homeomorphism

D'Onofrio

Schiattarella

2013

Advances in Calculus of Variations

Self Cite

View full text Add to dashboard Cite

Let R 2 be a domain. In 2007 Hencl, Koskela and Onninen proved that if f W onto ! 0 is a homeomorphism of bounded variation then so does its inverse map f 1 D .x; y/W 0 ! . In this paper we present a different proof giving precise formulae for the total variations of the coordinate functions of f 1 , that is,As an application, we prove that weak*-compactness in BV holds simultaneously for sequences of BV-homeomorphisms f j and their inverses f 1 j ; this symmetry result fails in the setting of bi-Sobolev mappings. We also deduce by the above formulae a slight generalization of a recent theorem of Iwaniec and Onninen on the existence a.e. of a right inverse of weak limit of W 1;2 -homeomorphisms. Extensions to higher dimension are given.

show abstract

“…Our technique are completely different; in fact we slice homeomorphism along coordinate directions. Theorem 1.7 generalizes the result of [4].…”

supporting

confidence: 51%

Section: Introductionmentioning

confidence: 87%

See 1 more Smart Citation

On the total variations for the inverse of a BV-homeomorphism

D'Onofrio

Schiattarella

2013

Advances in Calculus of Variations

Self Cite

View full text Add to dashboard Cite

show abstract

“…By results of [8], [9] and [13] we know that for f ∈ W 1,n−1 we have not only f −1 ∈ BV but also the total variation of the inverse satisfies…”

Section: Introductionmentioning

confidence: 99%

On distributional adjugate and derivative of the inverse

Hencl¹,

Kauranen²,

Malý³

2019

Preprint

View full text Add to dashboard Cite

Let Ω ⊂ R 3 be a domain and let f : Ω → R 3 be a bi-BV homeomorphism. Very recently in [16] it was shown that the distributional adjugate of Df (and thus also of Df −1 ) is a matrix-valued measure. In the present paper we show that the components of Adj Df are equal to components of Df −1 (f (U )) as measures and that the absolutely continuous part of the distributional adjugate Adj Df equals to the pointwise adjugate adj Df (x) a.e. We also show the equivalence of several approaches to the definition of the distributional adjugate.

show abstract

“…By results of [8,9,13] we know that for f ∈ W 1,n−1 we have not only f −1 ∈ BV but also the total variation of the inverse satisfies where adj A denotes the adjugate matrix to A, i.e. the matrix of (n − 1) × (n − 1) subdeterminants arranged in such a way that A adj A = I det A.…”

Section: Introductionmentioning

confidence: 99%

On distributional adjugate and derivative of the inverse

2021

View full text Add to dashboard Cite

Let Ω ⊂ R 3 be a domain and let f : Ω → R 3 be a bi-BV homeomorphism. Very recently in [16] it was shown that the distributional adjugate of Df (and thus also of Df −1 ) is a matrix-valued measure. In the present paper we show that the components of Adj Df coincide with the components of Df −1 (f (U )) as measures and that the absolutely continuous part of the distributional adjugate Adj Df equals to the pointwise adjugate adj Df (x) a.e. We also show the equivalence of several approaches to the definition of the distributional adjugate.

show abstract

Anisotropic Sobolev homeomorphisms

Cited by 18 publications

References 18 publications

On the total variations for the inverse of a BV-homeomorphism

On the total variations for the inverse of a BV-homeomorphism

On distributional adjugate and derivative of the inverse

On distributional adjugate and derivative of the inverse

Contact Info

Product

Resources

About