Related papers: Generalized $\mathbf{W^{1,1}}$-Young measures and …
Given a function $f\in C(\mathbb{R}^d)$ of linear growth, we give a new way of representing accumulation points of \begin{equation} \int_\Omega f(v_i(z))d\mu(z), \end{equation} where $\mu\in \mathcal{M}^+(\Omega)$, and $(v_i)_{i\in…
We characterize generalized Young measures, the so-called DiPerna-Majda measures which are generated by sequences of gradients. In particular, we precisely describe these measures at the boundary of the domain in the case of the…
This paper is devoted to the construction of generalized multi-scale Young measures, which are the extension of Pedregal's multi-scale Young measures [Trans. Amer. Math. Soc. 358 (2006), pp. 591-602] to the setting of generalized Young…
(Two-scale) gradient Young measures in Orlicz-Sobolev setting are introduced and characterized providing also an integral representation formula for non convex energies arising in homogenization problems with nonstandard growth.
Oscillations and concentrations in sequences of gradients $\{\nabla u_k\}$, bounded in $L^p(\Omega;\R^{M\times N})$ if $p>1$ and $\Omega\subset\R^n$ is a bounded domain with the extension property in $W^{1,p}$, and their interaction with…
This work presents a general principle, in the spirit of convex integration, leading to a method for the characterization of Young measures generated by gradients of maps in $W^{1,p}$ with $p$ less than the space dimension, whose Jacobian…
Using the generalized Young measure theory, we extend the theory of Young measure solutions to a class of quasilinear parabolic equations with linear growth, and introduce the concept of generalized Young measure solutions. We prove the…
We show that for constant rank partial differential operators $\mathscr{A}$, generalized Young measures generated by sequences of $\mathscr{A}$-free measures can be characterized by duality with $\mathscr{A}$-quasiconvex integrands of…
Motivated by variational problems in nonlinear elasticity depending on the deformation gradient and its inverse, we completely and explicitly describe Young measures generated by matrix-valued mappings $\{Y_k\}_{k\in\N} \subset…
We give two characterizations, one for the class of generalized Young measures generated by $\mathcal A$-free measures, and one for the class generated by $\mathcal B$-gradient measures $\mathcal Bu$. Here, $\mathcal A$ and $\mathcal B$ are…
In this contribution, we completely and explicitly characterize Young measures generated by gradients of quasiconformal maps in the plane. By doing so, we generalize the results of Astala and Faraco \cite{AstalaFaraco} who provided a…
This work is devoted to the study of two-scale gradient Young measures naturally arising in nonlinear elasticity homogenization problems. Precisely, a characterization of this class of measures is derived and an integral representation…
Being Omega an open and bounded Lipschitz domain of R^n, we consider the generalized Willmore functional on Omega defined, for smooth functions, as the p-Willmore energy of each isolevel set integrated over all levels. We propose a new…
We prove a characterization result in the spirit of the Kinderlehrer-Pedregal Theorem for Young measures generated by gradients of Sobolev maps satisfying the orientation-preserving constraint, that is the pointwise Jacobian is positive…
We study edge asymptotics of poissonized Plancherel-type measures on skew Young diagrams (integer partitions). These measures can be seen as generalizations of those studied by Baik--Deift--Johansson and Baik--Rains in resolving Ulam's…
This work presents a new proof of the recent characterization theorem for generalized Young measures generated by sequences in BV by Kristensen and the author [Arch. Ration. Mech. Anal. 197 (2010), 539-598]. The present argument is based on…
This work establishes a characterization theorem for (generalized) Young measures generated by symmetric derivatives of functions of bounded deformation (BD) in the spirit of the classical Kinderlehrer-Pedregal theorem. Our result places…
We characterize Young measures generated by gradients of bi-Lipschitz orientation-preserving maps in the plane. This question is motivated by variational problems in nonlinear elasticity where the orientation preservation and injectivity of…
We announce new existence and $\varepsilon$-regularity results for minimisers of the relaxation of strongly quasiconvex integrals that on smooth maps $u\colon\Omega\subset\mathbb{R}^{n}\to\mathbb{R}^{N}$ are defined by $$u\mapsto…
Generalized equations are problems emerging in contexts of modern variational analysis as an adequate formalism to treat such issues as constraint systems, optimality and equilibrium conditions, variational inequalities, differential…