Functions of bounded higher variation

By Robert L. Jerrard, H. M. Soner. 2002

96 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9eb4c81d8425eeae3b94208562553b9436230e97

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Local Currents in Metric Spaces (2011, background): “In this context we just mention the functions of bounded higher variation [8, 9, 21, 24, 27], the recent progress on (generalized) flat chains [1, 18, 36, 37], the scans from [10, 11, 16], the differentiation theory on metric measure spaces [4, 5, 22], and the derivations from [29, 30].”
Regularity of area minimizing currents I: gradient Lp estimates (2013, unknown): “[5, 22]) implies that this map has bounded variation in the metric sense introduced by Ambrosio in [4].”
Q-valued functions revisited (2008, background): “Indeed, by a key estimate of Jerrard and Soner (see [6] and [29]), the total variation of the slice map is controlled by the mass of T and ∂T .”
On the structure of the Sobolev space H1/2 with values into the circle (2000, unknown): “The last assertion in Theorem 1 is the H 1/2 -analogue of a result of Jerrard and Soner [15,16] (see also Hang and Lin [14]) concerning maps in W 1,1 (Ω; S 1 ).”
The interplay between analysis and topology in some nonlinear PDE problems (2003, background): “Remark 3. The conclusion that ’ is a constant (a.e.) may be related to a variety of results which have emerged in recent years in works of J. Bourgain, H. Brezis and P. Mironescu [10] [11] (see also H. Brezis [ 14 ]) about conditions implying that a given measurable function is constant.”
Functions with prescribed singularities (2003, background): “[ 28 ], Proposition 1 of section 5), although in this case it is more difficult to interpret the integersdi as degrees and the points xi as singularities.”
Lecture Notes on Optimal Transport Problems (2003, background): “Moreover, the 1-Wasserstein distance (corresponding to c(x, y )= |x − y| in (2)) is related to the so-called flat distance in Geometric Measure Theory, which plays an important role in its development (see [6], [24], [30], [ 27 ], [44]).”
Variational convergence for functionals of Ginzburg-Landau type. (2005, background): “We recall here some basic facts about Jacobians of Sobolev maps; see [3, 28] for further details and additional references.”
The Jacobian determinant revisited (2011, methodology): “Soner [27]) assumed that g ∈ W N−1 N ( ,SN−1); they used the same idea as in an earlier paper of J.”