Related papers: Regularity Properties of Constrained Set-Valued Ma…
In this paper, we establish a comprehensive characterization of the generalized Lipschitz classes through the study of the rate of convergence of a family of semi-discrete sampling operators, of Durrmeyer type, in $L^p$-setting. To achieve…
We obtain Lipschitz regularity results for a fairly general class of nonlinear first-order PDEs. These equations arise from the inner variation of certain energy integrals. Even in the simplest model case of the Dirichlet energy the…
In this paper, we study continuity and Lipschitzian properties of set-valued mappings, focusing on inner-type conditions. We introduce new notions of inner calmness* and, its relaxation, fuzzy inner calmness*. We show that polyhedral maps…
Let $F:[0,T]\times\R^n\mapsto 2^{\R^n}$ be a continuous multifunction with compact, not necessarily convex values. In this paper, we prove that, if $F$ satisfies the following Lipschitz Selection Property: \begin{itemize} \item[{(LSP)}]…
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We…
Over the past years a theory of conjugate duality for set-valued functions that map into the set of upper closed subsets of a preordered topological vector space was developed. For scalar duality theory, continuity of convex functions plays…
We consider the 1-harmonic flow of maps from a bounded domain into a submanifold of a Euclidean space, i.e. the gradient flow of the total variation functional restricted to maps taking values in the manifold. We restrict ourselves to…
In this paper we prove the local boundedness as well as the local Lipschitz continuity for solutions to a class of obstacle problems of the type $$\min\left\{\int_\Omega {F(x, Dz)}: z\in \mathcal{K}_{\psi}(\Omega)\right\}.$$ Here…
Newtonian spaces generalize first-order Sobolev spaces to abstract metric measure spaces. In this paper, we study regularity of Newtonian functions based on quasi-Banach function lattices. Their (weak) quasi-continuity is established,…
In this work, we establish regularity results for minimizers of the energy functional associated with the thin obstacle problem in Orlicz spaces. More precisely, we prove the Lipschitz continuity and the H\"older continuity of the gradient…
Denoting by $\mathbb{M}$ the complexification of the quaternionic algebra $\mathbb{H}$, we characterize the family of those $\mathbb{M}$-valued functions, defined on subsets of $\H$, whose values are actually quaternions, using an intrinsic…
We prove the local Lipschitz regularity of the local minimizers of scalar integral functionals of the form \begin{equation*} \mathcal{F}(v;\Omega)= \int_{\Omega} f (x, Dv) dx \end{equation*} under $(p,q)$-growth conditions. The main novelty…
We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…
We revisit the well-established regularity estimates on harmonic maps on surfaces to question their independence with respect to the dimension of the target manifold. We are mainly interested in harmonic maps into target ellipsoids, that we…
We study regularity properties of CR maps in positive codimension valued in pseudoconvex manifolds which carry a nontrivial Levi foliation. We introduce an invariant which can be used to deduce that any sufficiently regular CR map from a…
We consider a stochastic optimal control problem in a market model with temporary and permanent price impact, which is related to an expected utility maximization problem under finite fuel constraint. We establish the initial condition…
In the present paper, it was studied the boundary behavior of the so-called lower Q-homeomorphisms in the plane that are a natural generalization of the quasiconformal mappings. In particular, it was found a series of effective conditions…
In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Various calculus rules for these notions objects are…
In this paper, we study the regularity of several notions of Lipschitz solutions to the minimal surface system with an emphasis on partial regularity results. These include stationary solutions, integral weak solutions, and viscosity…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…