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On the structure of 𝓐-free measures and applications
We establish a general structure theorem for the singular part of 𝓐-free Radon measures,
where 𝓐 is a linear PDE operator. By applying the theorem to suitably chosen differential …
where 𝓐 is a linear PDE operator. By applying the theorem to suitably chosen differential …
[کتاب][B] Calculus of variations
F Rindler - 2018 - Springer
The calculus of variations has its roots in the first problems of optimality studied in classical
antiquity by Archimedes (ca. 287–212 BC in Syracuse, Magna Graecia) and Zenodorus (ca …
antiquity by Archimedes (ca. 287–212 BC in Syracuse, Magna Graecia) and Zenodorus (ca …
On rank one convex functions that are homogeneous of degree one
We show that positively 1-homogeneous rank one convex functions are convex at 0 and at
matrices of rank one. The result is a special case of an abstract convexity result that we …
matrices of rank one. The result is a special case of an abstract convexity result that we …
Characterization of Generalized Gradient Young Measures Generated by Sequences in W1,1 and BV
Generalized Young measures as introduced by DiPerna and Majda (Commun Math Phys
108: 667–689, 1987) provide a quantitative tool for studying the one-point statistics of …
108: 667–689, 1987) provide a quantitative tool for studying the one-point statistics of …
Characterization of Sobolev and BV spaces
Characterization of Sobolev and BV spaces Page 1 Journal of Functional Analysis 261 (2011)
2926–2958 www.elsevier.com/locate/jfa Characterization of Sobolev and BV spaces Giovanni …
2926–2958 www.elsevier.com/locate/jfa Characterization of Sobolev and BV spaces Giovanni …
Localization of nonlocal gradients in various topologies
In this paper, we study nonlocal gradients and their relationship to classical gradients. As the
nonlocality vanishes we demonstrate the convergence of nonlocal gradients to their local …
nonlocality vanishes we demonstrate the convergence of nonlocal gradients to their local …
Partial regularity for BV minimizers
We establish an ε ε-regularity result for the derivative of a map of bounded variation that
minimizes a strongly quasiconvex variational integral of linear growth, and, as a …
minimizes a strongly quasiconvex variational integral of linear growth, and, as a …
On the trace operator for functions of bounded 𝔸-variation
We consider the space BV 𝔸 (Ω) of functions of bounded 𝔸-variation. For a given first-order
linear homogeneous differential operator with constant coefficients 𝔸, this is the space of L 1 …
linear homogeneous differential operator with constant coefficients 𝔸, this is the space of L 1 …
Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints
We show general lower semicontinuity and relaxation theorems for linear-growth integral
functionals defined on vector measures that satisfy linear PDE side constraints (of arbitrary …
functionals defined on vector measures that satisfy linear PDE side constraints (of arbitrary …
Quasiconvex Functionals of (p, q)-Growth and the Partial Regularity of Relaxed Minimizers
We establish C∞-partial regularity results for relaxed minimizers of strongly quasiconvex
functionals F [u; Ω]:=∫ Ω F (∇ u) dx, u: Ω→ RN, subject to aq-growth condition| F (z)|≦ c …
functionals F [u; Ω]:=∫ Ω F (∇ u) dx, u: Ω→ RN, subject to aq-growth condition| F (z)|≦ c …