Related papers: Vectorial variational principles in $L^\infty$ and…

In this paper some qualitative and geometric aspects of nonsmooth vector fields theory are discussed. In the class of nonsmooth systems, that do not present sliding regions, a Poincar\'e-Bendixson Theorem is presented. A minimal set in…

We develop a theory of minors for alternating dimaps --- orientably embedded digraphs where, at each vertex, the incident edges (taken in the order given by the embedding) are directed alternately into, and out of, the vertex. We show that…

A formal methodology for developing variational principles corresponding to a given nonlinear PDE system is discussed. The scheme is demonstrated in the context of the incompressible Navier-Stokes equations, systems of first-order…

Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so called set relations. Contrary to the popular paradigm in vector optimization, the solution concept for such…

The primary goal of the paper is to establish characteristic properties of (extended) real-valued functions defined on normed vector spaces that admit the representation as the lower envelope of their minimal (with respect to pointwise…

We generalized the Korkin-Zolotarev theorem to the case of entire functions having the smallest $L^1$ norm on a system of intervals $E$. If $\bbC\setminus E$ is a domain of Widom type with the Direct Cauchy Theorem we give an explicit…

Variational principles are proved for self-adjoint operator functions arising from variational evolution equations of the form \[ \langle\ddot{z}(t),y \rangle + \mathfrak{d}[\dot{z} (t), y] + \mathfrak{a}_0 [z(t),y] = 0. \] Here…

We extend the variational approach to regularity for optimal transport maps initiated by Goldman and the first author to the case of general cost functions. Our main result is an $\epsilon$-regularity result for optimal transport maps…

We provide necessary and sufficient conditions for the uniqueness of minimisers of the Ginzburg-Landau functional for $\mathbb{R}^n$-valued maps under a suitable convexity assumption on the potential and for $H^{1/2} \cap L^\infty$ boundary…

For nonexpansive fixed-point problems, Halpern's method with optimal parameters, its so-called H-dual algorithm, and in fact, an infinite family of algorithms containing them, all exhibit the exactly minimax optimal convergence rates. In…

We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. We prove that we have convergence for all parameter values or divergence everywhere except for an exceptional set in the…

A class of causal variational principles on a compact manifold is introduced and analyzed both numerically and analytically. It is proved under general assumptions that the support of a minimizing measure is either completely timelike, or…

We prove existence and uniqueness of minimizers for a family of energy functionals that arises in Elasticity and involves polyconvex integrands over a certain subset of displacement maps. This work extends previous results by Awi and Gangbo…

This paper derives some discrete maximum principles for $P1$-conforming finite element approximations for quasi-linear second order elliptic equations. The results are extensions of the classical maximum principles in the theory of partial…

We develop a pseudo-likelihood theory for rank one matrix estimation problems in the high dimensional limit. We prove a variational principle for the limiting pseudo-maximum likelihood which also characterizes the performance of the…

We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…

This paper concerns generalized differential characterizations of maximal monotone set-valued mappings. Using advanced tools of variational analysis, we establish coderivative criteria for maximal monotonicity of set-valued mappings, which…

Optimal control problems are usually addressed with the help of the famous Pontryagin Maximum Principle (PMP) which gives a generalization of the classical Euler-Lagrange and Weierstrass necessary optimality conditions of the calculus of…

In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal…

Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, metric regularity can be elusive for some important ill-posed classes of problems…