Related papers: Relaxation of quasi-convex functionals with variab…
The most general operator product expansion in conformal field theory is obtained using the embedding space formalism and a new uplift for general quasi-primary operators. The uplift introduced here, based on quasi-primary operators with…
Starting from an energy comprised of both a bulk term and a surface term, set in the space of special functions of bounded hessian, $SBH$, a relaxation problem in the context of second-order structured deformations was studied in…
With the development of science, many nonlinear problems have emerged. At this time, the classical function space has certain restrictions. For example, it has lost its effectiveness for nonlinear problems under nonstandard growth…
In this paper, we address the bounded/unbounded determination of geodesically convex optimization on Hadamard spaces. In Euclidean convex optimization, the recession function is a basic tool to study the unboundedness, and provides the…
In this paper a quasi-linear elliptic equation in the whole Euclidean space is considered. The nonlinearity of the equation is assumed to have exponential growth or have critical growth in view of Trudinger-Moser type inequality. Under some…
We consider a class of nonconvex energy functionals that lies in the framework of the peridynamics model of continuum mechanics. The energy densities are functions of a nonlocal strain that describes deformation based on pairwise…
Finding efficient and provable methods to solve non-convex optimization problems is an outstanding challenge in machine learning and optimization theory. A popular approach used to tackle non-convex problems is to use convex relaxation…
We attempt to give a bird's eye view of the physical mechanisms leading to anomalous relaxation, and the relation of this phenomenon with anomalous diffusion and transport. Whereas in some cases these two notions are indeed deeply related,…
We use functional methods to compute one-loop effects in Heavy Quark Effective Theory. The covariant derivative expansion technique facilitates the efficient extraction of matching coefficients and renormalization group evolution equations.…
Recently, a non-linear model of viscoelasticity based on Rational Extended Thermodynamics was proposed in [arXiv:2312.05116]. This theory extends the evolution of the viscous stress beyond the linear framework of the Maxwell model to the…
In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…
We show that the local Burkholder functional $\mathcal B_K$ is quasiconvex. In the limit of $p$ going to 2 we find a class of non-polyconvex functionals which are quasiconvex on the set of matrices with positive determinant. In order to…
In this work, we introduce a new class of non-convex functions, called implicit concave functions, which are compositions of a concave function with a continuously differentiable mapping. We analyze the properties of their minimization by…
This article presents an arithmetic, called superposition relaxation, for bracketing the graph of a multivariate factorable function on a compact domain between a pair of underestimating and overestimating functions that are both separable.…
In this paper we explore the potential of the double phase functional in an image processing context. To this end, we study minimizers of the double phase energy for functions with bounded variation and show that this energy can be obtained…
A new and simple method for quasi-convex optimization is introduced from which its various applications can be derived. Especially, a global optimum under constrains can be approximated for all continuous functions.
This work develops a class of relaxations in between the big-M and convex hull formulations of disjunctions, drawing advantages from both. The proposed "P-split" formulations split convex additively separable constraints into P partitions…
This article is concerned with a gradient-flow approach to a Cahn-Hilliard model for viscoelastic phase separation introduced by Zhou et al. (Phys. Rev. E, 2006) in its variant with constant mobility. By means of time-incremental…
In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are quasi-convex. Some applications to special means of real…
We study homogenization by $\Gamma$-convergence of periodic nonconvex integrals when the integrand has quasiconvex growth with convex effective domain.