منابع مشابه
Weak notions of Jacobian determinant and relaxation
In this paper we study two weak notions of Jacobian determinant for Sobolev maps, namely the distributional Jacobian and the relaxed total variation, which in general could be different. We show some cases of equality and use them to give an explicit expression for the relaxation of some polyconvex functionals.
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Numerical examples demonstrated that a prescribed positive Jacobian determinant alone can not uniquely determine a diffeomorphism. It is conjectured that the uniqueness of a transformation can be assured by its Jacobian determinant and the curl-vector. In this work, we study the uniqueness problem analytically and propose an approach to the proof of the uniqueness of a transformation with presc...
متن کاملThe Characterization of the Regularity of the Jacobian Determinant in the framework of Potential spaces
We give necessary and suucient conditions on the parameters s 1 ; s 2 such that the Jacobian determinant extends to a bounded operator from _ H s1 p1 _ H s2 p2 : : : _ H sm pm into Z 0. Here all spaces are deened on R n and 2 m n. In almost all cases the regularity of the Jacobian determinant is calculated exactly.
متن کاملDensity not realizable as the Jacobian determinant of a bilipschitz map
Are every two separated nets in the plane bilipschitz equivalent? In the late 1990s, Burago and Kleiner and, independently, McMullen resolved this beautiful question negatively. Both solutions are based on a construction of a density function that is not realizable as the Jacobian determinant of a bilipschitz map. McMullen’s construction is simpler than the Burago–Kleiner one, and we provide a ...
متن کاملTetrahedral Element Shape Optimization via the Jacobian Determinant and Condition Number
We present a new shape measure for tetrahedral elements that is optimal in the sense that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume. We use this shape measure to formulate two optimization objective fun...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2010
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-010-0300-9