6533b859fe1ef96bd12b7763

RESEARCH PRODUCT

Approximation of W1, Sobolev homeomorphism by diffeomorphisms and the signs of the Jacobian

Ville TengvallDaniel CampbellStanislav Hencl

subject

Sobolev homeomorphismGeneral Mathematicsta111010102 general mathematicsA domain01 natural sciencesMeasure (mathematics)Homeomorphism010101 applied mathematicsSobolev spaceCombinatoricssymbols.namesakeIntegerJacobian matrix and determinantsymbolsPiecewise affine0101 mathematicsapproximationJacobianMathematics

description

Abstract Let Ω ⊂ R n , n ≥ 4 , be a domain and 1 ≤ p [ n / 2 ] , where [ a ] stands for the integer part of a. We construct a homeomorphism f ∈ W 1 , p ( ( − 1 , 1 ) n , R n ) such that J f = det ⁡ D f > 0 on a set of positive measure and J f 0 on a set of positive measure. It follows that there are no diffeomorphisms (or piecewise affine homeomorphisms) f k such that f k → f in W 1 , p .

yearjournalcountryeditionlanguage
2018-06-01Advances in Mathematics
https://doi.org/10.1016/j.aim.2018.04.017