Related papers: On the integral representation of variational func…
We prove an integral representation result for a class of variational functionals appearing in the framework of hierarchical systems of structured deformations via a global method for relaxation. Some applications to specific relaxation…
In this paper we study the integral representation in the space SBD(O) of special functions with bounded deformation of some L^1-norm lower semicontinuous functionals invariant with respect to rigid motions.
We present some relaxation and integral representation results for energy functionals in the setting of structured deformations, with special emphasis given to the case of multi-level structured deformations. In particular, we present an…
We prove an integral representation result for variational functionals in the space $BV^{\mathcal{B}}$ of functions with bounded $\mathcal{B}$-variation where $\mathcal{B}$ denotes a $k$-th order, $\mathbb{C}$-elliptic, linear homogeneous…
We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that…
In this paper we prove an integral representation formula for a general class of energies defined on the space of generalized special functions of bounded deformation ($GSBD^p$) in arbitrary space dimensions. Functionals of this type…
An integral representation result is obtained for the relaxation of a class of energy functionals depend- ing on two vector fields with different behaviors, which may appear in the context of image decomposition and thermochemical…
A variational representation for functionals of G-Brownian motion is established by a finite-dimensional approximate technique. As an application of the variational representation, we obtain a large deviation principle for stochastic flows…
Integral representation results are obtained for the relaxation of some classes of energy functionals depending on two vector fields with different behaviors, which may appear in the context of image decomposition and thermochemical…
The purpose of this paper is to establish a variational representation \log \E [e^{f(B)}] = \sup_h \E [f(B + \int_0^{\cdot} d<B>_s h_s) - 1/2 \int_0^1 h_s \cdot (d<B>_s h_s)] for functionals of the d-dimensional G-Brownian motion B. Here \E…
We show that a certain integral representation of the one-sided Skorokhod reflection of a continuous bounded variation function characterizes the reflection in that it possesses a unique maximal solution which solves the Skorokhod…
We study the relaxation of multiple integrals of the calculus of variations, where the integrands are nonconvex with convex effective domain and can take the value \infty. We use local techniques based on measure arguments to prove integral…
We give an extension of the theory of relaxation of variational integrals in classical Sobolev spaces to the setting of metric Sobolev spaces. More precisely, we establish a general framework to deal with the problem of finding an integral…
This article studies an integral representation of functionals of linear growth on metric measure spaces with a doubling measure and a Poincar\'e inequality. Such a functional is defined through relaxation, and it defines a Radon measure on…
It is shown that some class of differential inclusions has solutions that are defined and bounded for all real values of independent variable. Applications to dynamics are considered.
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
In this paper a new variational approach concerning functions (continuous) over Hilbert spaces is presented.
In this paper, we show how under the continuum hypothesis one can obtain an integral representation for elements of the topological dual of the space of functions of bounded variation in terms of Lebesgue and Kolmogorov-Burkill integrals.
In this article we prove a representation formula for non-negative generalized harmonic functions with respect to a subordinate Brownian motion in a general open set $D\subset \mathbb{R}^d$. We also study oscillation properties of quotients…
We provide the integral representation formula for the relaxation in $BV(\Omega; \mathbb{R}^M)$ with respect to strong convergence in $L^1(\Omega; \mathbb{R}^M)$ of a functional with a boundary contact energy term. This characterization is…