Related papers: Global Functional calculus, lower/upper bounds and…
The paper proposes a new algorithm for solving global univariate optimization problems. The algorithm does not require convexity of the target function. For a broad variety of target functions after performing (if necessary) several…
The present paper is intended to provide the basis for the study of weakly differentiable functions on rectifiable varifolds with locally bounded first variation. The concept proposed here is defined by means of integration by parts…
We study boundary values of harmonic functions in spaces of quasianalytic functionals and spaces of ultradistributions of non-quasianalytic type. As an application, we provide a new approach to H\"ormander's support theorem for…
We derive conditions that ensure the existence of a bounded $H_\infty$-calculus in weighted $L_p$-Sobolev spaces for closed extensions $\underline{A}_T$ of a differential operator $A$ on a conic manifold with boundary, subject to…
We construct algebras of pseudodifferential operators on a continuous family groupoid G that are closed under holomorphic functional calculus, contain the algebra of all pseudodifferential operators of order 0 on G as a dense subalgebra,…
We establish general sufficient conditions for exact (and global) regularity in the $\bar\partial$-Neumann problem on $(p,q)$-forms, $0 \leq p \leq n$ and $1\leq q \leq n$, on a pseudoconvex domain $\Omega$ with smooth boundary $b\Omega$ in…
This paper is devoted to present new error bounds of regularized gap functions for polynomial variational inequalities with exponents explicitly determined by the dimension of the underlying space and the number/degree of the involved…
Graph-based methods have been proposed as a unified framework for discrete calculus of local and nonlocal image processing methods in the recent years. In order to translate variational models and partial differential equations to a graph,…
A new scheme is proposed for dealing with the problem of singularities in General Relativity. The proposal is, however, much more general than this. It can be used to deal with manifolds of any dimension which are endowed with nothing more…
In view of training increasingly complex learning architectures, we establish a nonsmooth implicit function theorem with an operational calculus. Our result applies to most practical problems (i.e., definable problems) provided that a…
We consider semilinear higher order (in time) evolution inequalities posed in an exterior domain of the half-space $\mathbb{R}_+^N$, $N\geq 2$, and involving differential operators of the form $\mathcal{L}_\lambda =-\Delta +\lambda/|x|^2$,…
We prove existence, uniqueness and regularity results for mixed boundary value problems associated with fully nonlinear, possibly singular or degenerate elliptic equations. Our main result is a global H\"older estimate for solutions,…
This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…
In this article, the authors survey and review the studies of boundary value problems for regular functions in Clifford analysis, which include theoretical foundations and useful methods. Its theoretical bases consist of the generalized…
One of the very few mathematically rigorous nonlinear model reduction methods is the restriction of a dynamical system to a low-dimensional, sufficiently smooth, attracting invariant manifold. Such manifolds are usually found using local…
In this paper we introduce a general type of differential equations with piecewise constant argument (EPCAG), and consider the problem of backward continuation of solutions. We establish the existence of global integral manifolds of…
In this paper, via applying the method developed by A. Cianchi and V. Maz'ya, the author obtains the global boundedness of the gradient for solutions to Dirichlet and Neumann problems of a class of Schr\"odinger equations under the minimal…
The local $L^2$-mapping property of Fourier integral operators has been established in H\"ormander \cite{H} and in Eskin \cite{E}. In this paper, we treat the global $L^2$-boundedness for a class of operators that appears naturally in many…
A differential algebra of nonlinear generalized functions is presented as a tool for a wide range of nonsmooth nonlinear problems. The power of the differential algebra is used to do mathematical calculations or proofs; then the final…
This paper contains a set of lecture notes on manifolds with boundary and corners, with particular attention to the space of quantum states. A geometrically inspired way of dealing with these kind of manifolds is presented,and explicit…