Related papers: On Lipschitz semicontinuity properties of variatio…
We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range amongst those with unbalanced…
In this paper, we study the nonhomogeneous Dirichlet problem concerning general semilinear elliptic equations in divergence form. We establish that the boundary Lipschitz regularity of solutions under some more weaker conditions on the…
In recent years, several numerical methods for solving the unique continuation problem for the wave equation in a homogeneous medium with given data on the lateral boundary of the space-time cylinder have been proposed. This problem enjoys…
Linear Parameter-Varying (LPV) systems with piecewise differentiable parameters is a class of LPV systems for which no proper analysis conditions have been obtained so far. To fill this gap, we propose an approach based on the theory of…
We consider the stability of Robust Optimization problems with respect to perturbations in their uncertainty sets. We focus on Linear Optimization problems, including those with a possibly infinite number of constraints, also known as…
Fitzpatrick's variational representation of maximal monotone operators is here extended to a class of pseudo-monotone operators in Banach spaces. On this basis, the initial-value problem associated with the first-order flow of such an…
In this paper, we study an inverse problem for linear parabolic system with variable diffusion coefficients subject to dynamic boundary conditions. We prove a global Lipschitz stability for the inverse problem involving a simultaneous…
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…
We consider a generalized equation governed by a strongly monotone and Lipschitz single-valued mapping and a maximally monotone set-valued mapping in a Hilbert space. We are interested in the sensitivity of solutions w.r.t. perturbations of…
We use the scale of Besov spaces B^\alpha_{\tau,\tau}(O), \alpha>0, 1/\tau=\alpha/d+1/p, p fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains…
Inspired by recent developments in the theory of stability results in the context of certain wave type phenomena, we discuss abstract damped hyperbolic type equations given in a block operator matrix form with regards to asymptotic…
The convergence behavior of gradient methods for minimizing convex differentiable functions is one of the core questions in convex optimization. This paper shows that their well-known complexities can be achieved under conditions weaker…
We consider the Rademacher- and Sobolev-to-Lipschitz-type properties for arbitrary quasi-regular strongly local Dirichlet spaces. We discuss the persistence of these properties under localization, globalization, transfer to weighted spaces,…
The article is devoted to the development of numerical methods for solving variational inequalities with relatively strongly monotone operators. We consider two classes of variational inequalities related to some analogs of the Lipschitz…
In this paper we study second order master equations arising from mean field games with common noise over arbitrary time duration. A classical solution typically requires the monotonicity condition (or small time duration) and sufficiently…
This paper investigates general and generalized differentiation properties of the optimal value function associated with perturbed optimization problems. Fundamental results on nearly convex sets and functions in infinite-dimensional spaces…
This paper establishes comprehensive stability results for quasi-variational inequalities (QVIs) under monotone perturbations of the governing operator. We prove strong convergence of both minimal and maximal solutions when sequences of…
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are…
Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in…
The aim of this note is to present some new results concerning "almost everywhere" well-posedness and stability of continuity equations with measure initial data. The proofs of all such results can be found in \cite{amfifrgi}, together with…