Related papers: Vector variational problem with knitting boundary …
In this paper we consider the Virtual Element discretization of a minimal surface problem, a quasi-linear elliptic partial differential equation modeling the problem of minimizing the area of a surface subject to a prescribed boundary…
We introduce a variational algorithm, which solves the classical inverse Sturm-Liouville problem when two spectra are given. In contrast to other approaches, it recovers the potential as well as the boundary conditions without a priori…
We consider the volume-constrained minimization of the sum of the perimeter and the Riesz potential. We add an external potential of the form $\|x\|^{\beta}$ that provides the existence of a minimizer for any volume constraint, and we study…
In this work, we study the reduction by a Lie group of symmetries of variational collision avoidance probelms of multiple agents evolving on a Riemannian manifold and derive necessary conditions for the reduced extremals. The problem…
We obtain a sharp lower bound on the isoperimetric deficit of a general polygon in terms of the variance of its side lengths, the variance of its radii, and its deviation from being convex. Our technique involves a functional minimization…
The discussion of our recent work concerning the vector solution of boundary-value problems in electromagnetism is extended to the case of no azimuthal symmetry by means of the spin-weighted spherical harmonics.
Source conditions are a key tool in regularisation theory that are needed to derive error estimates and convergence rates for ill-posed inverse problems. In this paper, we provide a recipe to practically compute source condition elements as…
Whereas in a coordinate-dependent setting the Euler-Lagrange equations establish necessary conditions for solving variational problems in which both the integrands of functionals and the resulting paths are assumed to be sufficiently…
We consider the variational problem consisting of minimizing a polyconvex integrand for maps between manifolds. We offer a simple and direct proof of the existence of a minimizing map. The proof is based on Young measures.
A Kac-Moody algebra construction for the integrable hierarchy containing the Gardner equation is proposed. Solutions are systematically constructed employing the dressing method and deformed vertex operators which takes into account the…
Variational inequalities are an important mathematical tool for modelling free boundary problems that arise in different application areas. Due to the intricate nonsmooth structure of the resulting models, their analysis and optimization is…
We consider the topic of linearization of finite elasticity for pure traction problems. We characterize the variational limit for the approximating sequence of rescaled nonlinear elastic energies. We show that the limiting minimal value can…
We consider a nonlinear boundary value problem driven by a nonhomogeneous differential operator. The problem exhibits competing nonlinearities with a superlinear (convex) contribution coming from the reaction term and a sublinear (concave)…
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
In this article we study constrained variational problems in one independent variable defined on the space of integral curves of a Frenet system in a homogeneous space G/H. We prove that if the Lagrangian is G-invariant and coisotropic then…
Diffusion of a penetrating liquid in a polymeric material does not often satisfy the classical diffusion equations and requires taking relaxational (viscoelastic) properties of the polymer into account. We investigate a boundary value…
The variational principle for a thin dust shell in General Relativity is constructed. The principle is compatible with the boundary-value problem of the corresponding Euler-Lagrange equations, and leads to ``natural boundary conditions'' on…
In this paper, we study a maximization and a minimization problem associated with a Poisson boundary value problem. Optimal solutions in a set of rearrangements of a given function define stationary and stable flows of an ideal fluid in two…
We study the least gradient problem in bounded regions with Lipschitz boundary in the plane. We provide a set of conditions for the existence of solutions in non-convex simply connected regions. We assume the boundary data is continuous and…
This paper is devoted to the problem of prescribing the scalar curvature under zero boundary conditions. Using dynamical and topological methods involving the study of critical points at infinity of the associated variational problem, we…