Related papers: Existence of Weak Solutions for Non-Simple Elastic…

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…

We consider a thin elastic strip of thickness h and we show that stationary points of the nonlinear elastic energy (per unit height) whose energy is of order h^2 converge to stationary points of the Euler-Bernoulli functional. The proof…

In this paper, we demonstrate the existence of positive solutions for certain weakly coupled elliptic systems of sublinear growth under homogeneous Dirichlet boundary conditions. Our findings generalize existing results related to sublinear…

Surface growth is a crucial component of many natural and artificial processes from cell proliferation to additive manufacturing. In elastic systems surface growth is usually accompanied by the development of geometrical incompatibility…

We discuss a notion of weak solution for a semilinear wave equation that models the interaction of an elastic body with a rigid substrate through an adhesive layer, relying on results in [2]. Our analysis embraces the vector-valued case in…

We explore local existence and properties of classical weak solutions to the initial-boundary value problem of a one-dimensional quasilinear equation of elastodynamics with non-convex stored-energy function, a model of phase transitions in…

In this paper, we consider weak solutions of the Euler-Lagrange equation to a variational energy functional modeling the geometrically nonlinear Cosserat micropolar elasticity of continua in dimension three, which is a system coupling…

For two different scenarios regarding thin elastic structures, described by 2d-F\"oppl-von K\'arm\'an plate models, we obtain energy scaling laws. Firstly, assuming the reference geometry being that of a singular excess-cone, we obtain…

Isothermal visco-elastodynamics in the Kelvin-Voigt rheology is formulated in the spatial Eulerian coordinates in terms of velocity and deformation gradient. A generally nonconvex (possibly also frame-indifferent) stored energy is admitted.…

We propose models in nonlinear elasticity for nonsimple materials that include surface energy terms. Additionally, we also discuss living surface loads on the boundary. We establish corresponding linearized models and show their…

In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, $\mathbb{R}^k$. We prove the $\Gamma$-convergence of elastic energies for configurations of a converging…

We derive local boundedness estimates for weak solutions of a large class of second order quasilinear equations. The structural assumptions imposed on an equation in the class allow vanishing of the quadratic form associated with its…

Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions of Riemannian manifolds into the Euclidean spaces (see Ciarlet [9,10]). In this paper, we study the rigidity and continuity properties of…

In [12], the authors studied a particular class of equilibrium solutions of the Helfrich energy which satisfy a second order condition called the reduced membrane equation. In this paper we develop and apply a second variation formula for…

Lipid bilayer membranes are commonly modeled as area-preserving fluid surfaces that resist bending. There appear to be two schools of thought in the literature concerning the actual area constraint. In some works the total or global area…

The deformation problem for a transversely isotropic elastic layer bonded to a rigid substrate and coated with a very thin elastic layer made of another transversely isotropic material is considered. The leading-order asymptotic models (for…

We analyze the pressureless Navier-Stokes system with nonlocal attraction-repulsion forces. Such systems appear in the context of models of collective behavior. We prove the existence of weak solutions on the whole space $\mathbb{R}^3$ in…

We consider the problem of energy decay rates for nonlinearly damped abstract infinite dimensional systems. We prove sharp, simple and quasi-optimal energy decay rates through an indirect method, namely a weak observability estimate for the…

We extend the theory of structured deformations to the setting of linearized elasticity by providing an integral representation for the underlying energy that features bulk and surface contributions. Our derivation is obtained both via a…

Functionalized thin elastic films and membranes frequently feature internal sites of net forces or stresses. These are, for instance, active sites of actuation, or rigid inclusions in a strained membrane that induce counterstress upon…