Results 21 to 30 of about 76 (75)

Explicit Bounds and Sharp Results for the Composition Operators Preserving the Exponential Class

Journal of Function Spaces, Volume 2016, Issue 1, 2016., 2016
Let f:Ω⊂Rn→Rn be a quasiconformal mapping whose Jacobian is denoted by Jf and let EXP(Ω) be the space of exponentially integrable functions on Ω. We give an explicit bound for the norm of the composition operator Tf: u ∈ EXP(Ω) ↦ u∘f−1 ∈ EXP(f(Ω)) and, as a related question, we study the behaviour of the norm of log⁡Jf in the exponential class.
Fernando Farroni, Raffaella Giova, Stanislav Hencl   +2 more
wiley   +1 more source

Approximate Limit, Approximate Derivative, and Approximate Integral for Fuzzy‐Number‐Valued Functions

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This paper introduces the concepts of approximate limit, approximate continuity, and approximate derivatives for fuzzy‐number‐valued functions and examines their fundamental properties. Also, the relationships between approximate limit, approximate derivative of fuzzy‐number‐valued functions, and their representations of λ‐level sets are investigated ...
Chao Ma, Zengtai Gong, Yabin Shao, Ömer Kişi   +3 more
wiley   +1 more source

Multiplicity of Solutions for Schrödinger Equations with Concave‐Convex Nonlinearities

International Journal of Analysis, Volume 2016, Issue 1, 2016., 2016
We study the multiplicity of solutions for a class of semilinear Schrödinger equations: -Δu+V(x)u=gx,u, for x∈RN; u(x)→0, as u→∞, where V satisfies some kind of coercive condition and g involves concave‐convex nonlinearities with indefinite signs. Our theorems contain some new nonlinearities.
Dong-Lun Wu, Chun-Lei Tang, Xing-Ping Wu, Dong Ye   +3 more
wiley   +1 more source

On a Theorem of Banach and Kuratowski and $K$-Lusin Sets

Rocky Mountain Journal of Mathematics, 2003
In a paper of 1929, Banach and Kuratowski proved, assuming the continuum hypothesis, a combinatorial theorem which implies that there is no non-vanishing sigma-additive finite measure on the real line which is defined for every set of reals. It will be shown that the combinatorial theorem is equivalent to the existence of a K-Lusin set of size the ...
Halbeisen, Lorenz, Bartoszynski, T.
openaire   +4 more sources

Second‐order regularity for degenerate p$p$‐Laplace type equations with log‐concave weights

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract We consider weighted p$p$‐Laplace type equations with homogeneous Neumann boundary conditions in convex domains, where the weight is a log‐concave function which may degenerate at the boundary. In the case of bounded domains, we provide sharp global second‐order estimates. For unbounded domains, we prove local estimates at the boundary.
Carlo Alberto Antonini, Giulio Ciraolo, Francesco Pagliarin   +2 more
wiley   +1 more source

Monotone versus non‐monotone projective operators

Bulletin of the London Mathematical Society, Volume 57, Issue 1, Page 256-264, January 2025.
Abstract For a class of operators Γ$\Gamma$, let |Γ|$|\Gamma |$ denote the closure ordinal of Γ$\Gamma$‐inductive definitions. We give upper bounds on the values of |Σ2n+11,mon|$|\Sigma ^{1,mon}_{2n+1}|$ and |Π2n+21,mon|$|\Pi ^{1,mon}_{2n+2}|$ under the assumption that all projective sets of reals are determined, significantly improving the known ...
J. P. Aguilera, P. D. Welch
wiley   +1 more source

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
wiley   +1 more source

Bayesian social aggregation with almost‐objective uncertainty

Theoretical Economics, Volume 19, Issue 3, Page 1351-1398, July 2024.
We consider collective decisions under uncertainty, when agents have generalized Hurwicz preferences, a broad class allowing many different ambiguity attitudes, including subjective expected utility preferences. We consider sequences of acts that are “almost‐objectively uncertain” in the sense that asymptotically, all agents almost agree about the ...
Marcus Pivato, Élise Flore Tchouante
wiley   +1 more source

The Lusin Theorem and Horizontal Graphs in the Heisenberg Group

Analysis and Geometry in Metric Spaces, 2013
Abstract In this paper we prove that every collection of measurable functions fα , |α| = m, coincides a.e. withmth order derivatives of a function g ∈ Cm−1 whose derivatives of order m − 1 may have any modulus of continuity weaker than that of a Lipschitz function.
Hajłasz Piotr, Mirra Jacob
openaire   +4 more sources

A Quantitative Lusin Theorem for Functions in BV [PDF]

, 2015
We extend to the BV case a measure theoretic lemma previously proved by DiBenedetto et al. (Atti Accad. Naz. Lincei Cl. Sci. Mat. Appl. 9, 223–225, 2006) in W loc 1, 1. It states that if the set where u is positive occupies a sizable portion of an open set E then the set where u is positive clusters about at least one point of E. In this note we follow
Telcs, Andras, VESPRI, VINCENZO
openaire   +2 more sources