Related papers: An axiomatic approach to gradients with applicatio…

We study existence and uniqueness of solutions for second order ordinary stochastic differential equations with Dirichlet boundary conditions on a given interval. In the first part of the paper we provide sufficient conditions to ensure…

The paper concerns foundations of sensitivity and stability analysis in optimization and related areas, being primarily addressed truncated constrained systems. We consider general models, which are described by multifunctions between…

We carry out a systematic study of decidability for theories of (a) real vector spaces, inner product spaces, and Hilbert spaces and (b) normed spaces, Banach spaces and metric spaces, all formalised using a 2-sorted first-order language.…

We derive sufficient criteria for the uniqueness and existence of solutions of the abstract Cauchy problem in locally convex Hausdorff spaces. Our approach is based on a suitable notion of an asymptotic Laplace transform and extends results…

We prove the existence of measurable invariant manifolds for small perturbations of linear Random Dynamical Systems evolving on a Banach space and admitting a general type of dichotomy, both for continuous and discrete time. Moreover, the…

The theory of Banach spaces of Dirichlet series has drawn an increasing attention in the recent 25 years. One of the main interest of this new theory is that of defining analogues of the classical spaces of analytic functions on the unit…

In this paper, we consider the Dirichlet problem for a class of Hessian quotient equations on Riemannian manifolds. Under the assumption of an admissible subsolution, we solve the existence and the uniquness for the Dirichlet problem in a…

In these notes of lectures at the 2004 Summer School of Mathematical Physics in Ravello, Italy, the author develops an approach to calculus in which more efficient choices of limits are taken at key points of the development. For example,…

In this paper we study a Dirichlet-type differential inclusion involving the Finsler-Laplace operator on a complete Finsler manifold. Depending on the positive $\lambda$ parameter of the inclusion, we establish non-existence, as well as…

The Herglotz problem is a generalization of the fundamental problem of the calculus of variations. In this paper, we consider a class of non-differentiable functions, where the dynamics is described by a scale derivative. Necessary…

The present contribution investigates shape optimisation problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and material derivatives are firstly derived in an…

We consider a random variable $Y$ and approximations $Y\_n$, defined on the same probability space with values in the same measurable space as $Y$. We are interested in situations where the approximations $Y\_n$ allow to define a Dirichlet…

The aim of the paper is to show that the solutions to variational problems with non-standard growth conditions satisfy a corresponding variational inequality without any smallness assumptions on the gap between growth and coercitivity…

In this paper we prove existence of (viscosity) solutions of Dirichlet problems concerning fully nonlinear elliptic operator, which are either degenerate or singular when the gradient of the solution is zero. For this class of operators it…

In this manuscript we deal with existence/uniqueness and regularity issues of suitable weak solutions to nonlocal problems driven by fractional Laplace type operators. Different from previous researches, in our approach we consider gradient…

The aim of this note is to provide several variants of the diameter two properties for Banach spaces. We study such properties looking for the abundance of diametral points, which holds in the setting of Banach spaces with the Daugavet…

We investigate the variational structure of discrete Laplace-type equations that are motivated by discrete integrable quad-equations. In particular, we explain why the reality conditions we consider should be all that are reasonable, and we…

We prove that the spatial gradient of (variational) solutions to parabolic obstacle problems of p-Laplacian type enjoys the same regularity of the data and of the derivatives of the obstacle in the scale of Lorentz spaces.

A variant of the abstract Cauchy-Kovalevskaya theorem is considered. We prove existence and uniqueness of classical solutions to the nonlinear, non-autonomous initial value problem \[ \frac{du(t)}{dt} = A(t)u(t) + B(u(t),t), \ \ u(0) = x \]…

This paper is a continuation of our ongoing efforts to solve a number of geometric problems and their extensions by using advanced tools of variational analysis and generalized differentiation. Here we propose and study, from both…