English
Related papers

Related papers: Relaxation of quasi-convex functionals with variab…

200 papers

The aim of this paper is to study a wide class of non-convex sweeping processes with moving constraint whose translation and deformation are represented by regulated functions, i.e., functions of not necessarily bounded variation admitting…

Dynamical Systems · Mathematics 2021-01-08 Pavel Krejci , Giselle Antunes Monteiro , Vincenzo Recupero

We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of…

Analysis of PDEs · Mathematics 2020-11-04 Nassif Ghoussoub , Young-Heon Kim , Hugo Lavenant , Aaron Zeff Palmer

Variational problems of splitting-type with mixed linear-superlinear growth conditions are considered. In the twodimensional case the minimizing problem is given by \[ J [w] = \int_{\Omega} \Big[f_1\big(\partial_1 w\big) +…

Analysis of PDEs · Mathematics 2020-07-30 Michael Bildhauer , Martin Fuchs

We study the convex lift of Mumford-Shah type functionals in the space of rectifiable currents and we prove a generalized coarea formula in dimension one, for finite linear combinations of SBV graphs. We use this result to prove the…

Analysis of PDEs · Mathematics 2017-09-29 Marcello Carioni

In this paper we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational…

Numerical Analysis · Mathematics 2023-09-11 Anna Ochal , Wiktor Prządka , Mircea Sofonea , Domingo A. Tarzia

The existence of a homogeneous decomposition for continuous and epi-translation invariant valuations on super-coercive functions is established. Continuous and epi-translation invariant valuations that are epi-homogeneous of degree $n$ are…

Metric Geometry · Mathematics 2020-05-15 A. Colesanti , M. Ludwig , F. Mussnig

We study convex relaxations of nonconvex quadratic programs. We identify a family of so-called feasibility preserving convex relaxations, which includes the well-known copositive and doubly nonnegative relaxations, with the property that…

Optimization and Control · Mathematics 2023-03-14 E. Alper Yildirim

We propose in this paper a proximal and contraction method for solving a convex mixed variational inequality problem in a real Hilbert space. To accelerate the convergence of our proposed method, we incorporate an inertial extrapolation…

Optimization and Control · Mathematics 2025-11-25 Chidi Elijah Nwakpa , Austine Efut Ofem , Kalu Okam Okorie , Chinedu Izuchukwu , Chibueze Christian Okeke

We present a comprehensive theoretical analysis of the stress relaxation in a multiply but weakly buckled incompressible rod in a viscous solvent. In the bulk two interesting regimes of generic self--similar intermediate asymptotics are…

Soft Condensed Matter · Physics 2007-05-23 Oskar Hallatschek , Erwin Frey , Klaus Kroy

The theory of quasi-linear viscoelasticity (QLV) is modified and developed for transversely isotropic (TI) materials under finite deformation. For the first time, distinct relaxation responses are incorporated into an integral formulation…

Soft Condensed Matter · Physics 2018-11-05 Valentina Balbi , Tom Shearer , William J Parnell

The purpose of this paper is to study the lower semicontinuity with respect to the strong $L^1$-convergence, of some integral functionals defined in the space SBD of special functions with bounded deformation. Precisely, let $U$ be a…

Functional Analysis · Mathematics 2007-05-23 Francois Ebobisse

We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…

Optimization and Control · Mathematics 2024-01-02 Valerian-Alin Fodor , Nicolae Popovici

We study a model for the deformation of a visco-elasto-plastic material that is nearly incompressible. It originates from geophysics, is given in the Eulerian description and combines a Kelvin-Voigt rheology in the spherical part with a…

Analysis of PDEs · Mathematics 2025-12-22 Thomas Eiter

The aim of this paper is to extend previous results regarding the multiplicity of solutions for quasilinear elliptic problems with critical growth to the variable exponent case. We prove, in the spirit of \cite{DPFBS}, the existence of at…

Analysis of PDEs · Mathematics 2009-12-18 Analía Silva

This paper deals with some nonlinear problems which exponential and biexponential decays are involved in. A proof of the quasiconvexity of the error function in some of these problems of optimization is presented. This proof is restricted…

Concentrated forces acting at the tip of a two-dimensional wedge give rise to the classical Flamant solution to linear elasticity, whose displacement and strain are singular at the tip of the wedge. Starting from nonlinear elasticity, we…

Analysis of PDEs · Mathematics 2026-05-19 Dominik Engl , Paul Plucinsky , Ian Tobasco

A class of real functions, which is the generalization of a family of convex functions, is introduced; in this connection, we have defined $X$-convex, strictly $X$-convex, quasi-$X$-convex, strictly quasi-$X$-convex, and semi-strictly…

Optimization and Control · Mathematics 2022-08-16 Musavvir Ali , Ehtesham Akhter

Recently, Kulikov (\cite{Ku}) has shown that certain convex functionals on weighted Bergman spaces are maximized by reproducing kernels. We show a sharp quantitative stability of these estimates with the optimal norm and the exponent and an…

Classical Analysis and ODEs · Mathematics 2025-12-04 Petar Melentijević

We consider a class of ordinary differential equations describing one-dimensional quasiperiodically forced systems in the presence of large damping. We give a fully constructive proof of the existence of response solutions, that is…

Dynamical Systems · Mathematics 2014-03-24 Guido Gentile

In this paper we prove that the Anzellotti pairing can be regarded as a relaxed functional with respect to the weak* convergence in the space BV of functions of bounded variation. The crucial tool is a preliminary integral representation of…

Functional Analysis · Mathematics 2024-10-11 Graziano Crasta , Virginia De Cicco