Quasiregular mappings in even dimensions

Iwaniec, Tadeusz; Martin, Gaven

doi:10.1007/bf02392454

Cited by 187 publications

(140 citation statements)

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“…The existence of such quasiconvex functions has been established in Müller,Šverák and Yan [20], and Yan and Zhou [29], following important work of Iwaniec [11], Iwaniec and Sbordone [15] and Iwaniec and Martin [14].…”

Section: Du(x) ∈ K L Ae X ∈ ωmentioning

confidence: 99%

“…2) The special case when n is even and L = 1 has been considered by Müller,Šverák and Yan in [20], using a special linear structure of the conformal set K 1 and following the important work of Iwaniec and Martin [14].…”

Section: Theorem 22 ([20] [30]) Letmentioning

confidence: 99%

“…We recall that (see, e.g., Astala [2], Iwaniec [11], Iwaniec and Martin [14]) a map u from a domain Ω in R n to R n is said to be weakly Lquasiregular, L ≥ 1 being a constant called the (outer) dilatation of u, if it belongs to a (local) Sobolev space W 1,p loc (Ω; R n ) for some p ≥ 1 and satisfies…”

Section: Introductionmentioning

confidence: 99%

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A linear boundary value problem for weakly quasiregular mappings in space

Yan¹

2001

Calculus of Variations and Partial Differential Equations

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Abstract. Given a number L ≥ 1, a weakly L-quasiregular map on a domain Ω in space R n is a map u in a Sobolev spaceIn this paper, we study the problem concerning linear boundary values of weakly L-quasiregular mappings in space R n with dimension n ≥ 3. It turns out this problem depends on the power p of the underlying Sobolev space. For p not too far below the dimension n we show that a weakly quasiregular map in W 1,p (Ω; R n ) can only assume a quasiregular linear boundary value; however, for all L ≥ 1 and 1 ≤ p < nL L+1 , we prove a rather surprising existence result that every linear map can be the boundary value of a weakly L-quasiregular map in W 1,p (Ω; R n ). Classification (1991):30C65, 30C70, 35F30, 49J30 Mathematics Subject

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Section: Du(x) ∈ K L Ae X ∈ ωmentioning

confidence: 99%

Section: Theorem 22 ([20] [30]) Letmentioning

confidence: 99%

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A linear boundary value problem for weakly quasiregular mappings in space

Yan¹

2001

Calculus of Variations and Partial Differential Equations

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“…Let n = m = k ≥ 2 and for L ≥ 1 let N (X ) = Ln n=2 det X: We can then recover from Theorems 7.1 and 7.3 some of results in [17,19,33,37] concerning the regularity of the so-called weakly L-quasiregular mappings.…”

Section: Some Examples and Applicationsmentioning

confidence: 86%

Lp-Mean coercivity, regularity and relaxation in the calculus of variations

Yan

Zhou

2001

Nonlinear Analysis: Theory, Methods & Applications

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“…This is determined by the sharpness of the bounds in equation (1.2). In fact, Iwaniec and Martin previously conjectured [IM93] that in R n , n ≥ 2, sets with Hausdorff measure Theorem 1.2. (a) Consider the statement (1.3), i.e.…”

Section: Introductionmentioning

confidence: 99%