Results 71 to 80 of about 73,971 (227)
Upper Semicontinuous Decompositions of the n-Sphere [PDF]
Proceedings of the American Mathematical Society, 1962 We consider conditions under which an upper semicontinuous decomposition has the decomposition space which is a topological nsphere. A special emphasis is placed on the case in which the decomposition has only a countable number of nondegenerate elements.
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Seminormality and upper semicontinuity in optimal control [PDF]
Journal of Optimization Theory and Applications, 1970 This paper concerns the concept of upper semicontinuity of variable sets, precisely the variant of Kuratowski's definition of upper semicontinuity that Cesari has denoted as property (Q). This concept has been used by Cesari in most of his papers on existence theorems for optimal solutions, and later used by Olech, Lasota and Olech, Brunovsky, Baum ...
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Piecewise rank‐one approximation of vector fields with measure derivatives
Bulletin of the London Mathematical Society, Volume 57, Issue 1, Page 181-202, January 2025.Abstract This work addresses the question of density of piecewise constant (resp. rigid) functions in the space of vector‐valued functions with bounded variation (resp. deformation) with respect to the strict convergence. Such an approximation property cannot hold when considering the usual total variation in the space of measures associated to the ...
Jean‐François Babadjian +1 more
wiley +1 more source
Study of ODE limit problems for reaction-diffusion equations [PDF]
Opuscula Mathematica, 2018 In this work we study ODE limit problems for reaction-diffusion equations for large diffusion and we study the sensitivity of nonlinear ODEs with respect to initial conditions and exponent parameters.
Jacson Simsen +2 more
doaj +1 more source
On the upper and lower semicontinuity of the Aumann integral [PDF]
Journal of Mathematical Economics, 1990 Abstract Let ( T ,τ,μ) be a finite measure space, X be a Banach space, P be a metric space and let L 1 (μ, X ) denote the space of equivalence classes of X -valued Bochner integrable functions on ( T ,τ,μ). We show that if φ: T × P →2 X is a set-valued function such that for each fixed p ϵ P , φ(·, p ) has a measurable graph and for each ...
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Harmonic balls in Liouville quantum gravity
Proceedings of the London Mathematical Society, Volume 130, Issue 1, January 2025.Abstract Harmonic balls are domains that satisfy the mean‐value property for harmonic functions. We establish the existence and uniqueness of harmonic balls on Liouville quantum gravity (LQG) surfaces using the obstacle problem formulation of Hele–Shaw flow.
Ahmed Bou‐Rabee, Ewain Gwynne
wiley +1 more source
Upper-semicontinuity of the global attractors for a class of nonlocal Cahn-Hilliard equations [PDF]
arXiv, 2018 The aim of this work is to examine the upper-semicontinuity properties of the family of global attractors admitted by a non-isothermal viscous relaxation of some nonlocal Cahn-Hilliard equations. We prove that the family of global attractors is upper-semicontinuous as the perturbation parameters vanish.
arxiv
Carnot rectifiability and Alberti representations
Proceedings of the London Mathematical Society, Volume 130, Issue 1, January 2025.Abstract A metric measure space is said to be Carnot‐rectifiable if it can be covered up to a null set by countably many bi‐Lipschitz images of compact sets of a fixed Carnot group. In this paper, we give several characterisations of such notion of rectifiability both in terms of Alberti representations of the measure and in terms of differentiability ...
G. Antonelli, E. Le Donne, A. Merlo
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On Shape Optimization Theory With Fractional p‐Laplacian Operators
Abstract and Applied Analysis, Volume 2025, Issue 1, 2025.The focus of this paper is the investigation of shape optimization problems with operators such as fractional Laplacian and p‐Laplacian operators, that is, (−Δ)s and −Δps, where 0 < s < 1 and p ≥ 2. In the admissible set of s− quasi‐open, the existence of optimal shape is proved for shape derivative of the functional F(Ω) = f(Ω, uΩ), where uΩ ...
Malick Fall +4 more
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On Perturbed Weak Vector Equilibrium Problems under new Semi-continuities [PDF]
arXiv, 2017 In this paper we introduce a new semicontinuity notion, which is weaker than upper semicontinuity, and assures the closedness of the sets $G(y)=\{x\in K: f(x,y)\not\in -\inte C\}.$ Furhter, this semicontinuity is also closed under addition. These two properties make our new semicontinuity applicable in situations where other semicontinuities, like ...
arxiv