Article
Mathematics, Applied
Jae Hyoung Lee, Tien-Son Pham
Summary: In this paper, properties of semialgebraic set-valued maps with closed graphs are studied, including the equivalence between open mapping and locally closed range. Through Robinson's normal map formulation, results in the context of semialgebraic variational inequalities are derived. The study also shows the equivalence between openness and nonextremality for continuous single-valued maps from Rn to R.
SIAM JOURNAL ON OPTIMIZATION
(2022)
Article
Mathematics
Tiziano Granucci
Summary: This paper studies the everywhere Holder continuity of the minima of a class of vectorial integral functionals. By analyzing the properties of each component, the regularity of the minima and the Holder continuity are obtained.
MONATSHEFTE FUR MATHEMATIK
(2023)
Article
Mathematics, Applied
Nikolaos S. Papageorgiou, Youpei Zhang
Summary: The study explores a nonlinear Robin problem driven by the (p, q)-Laplacian and a parametric reaction. It demonstrates a bifurcation-type theorem describing changes in positive solution sets with the parameter lambda on the range (0, +infinity). Additionally, the continuity properties of the solution multifunction are determined.
ADVANCES IN NONLINEAR ANALYSIS
(2021)
Article
Mathematics, Applied
Christopher S. Goodrich
Summary: This article focuses on minimizers of a functional integral, refining growth estimates by imposing restrictions on the coefficient, which improves the matching of results to specific problems compared to existing literature.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Alessandro Audrito
Summary: We prove uniform parabolic Holder estimates of De Giorgi-Nash-Moser type for sequences of minimizers of functionals. As a consequence, we deduce the existence and Holder regularity of weak solutions to a class of weighted nonlinear CauchyNeumann problems arising in combustion theory and fractional diffusion.
JOURNAL OF EVOLUTION EQUATIONS
(2023)
Article
Operations Research & Management Science
Fedor Stonyakin, Alexander Gasnikov, Pavel Dvurechensky, Alexander Titov, Mohammad Alkousa
Summary: We introduce an inexact oracle model for variational inequalities with monotone operators, propose a numerical method that solves such variational inequalities, and analyze its convergence rate. We also extend the algorithm to variational inequalities with strongly monotone operators and apply it to convex-concave saddle point problems with Holder-continuous partial subgradients.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2022)
Article
Mathematics
Panagiotis Polymerakis
Summary: This study demonstrates the existence of non-constant positive harmonic functions under certain conditions.
ADVANCES IN MATHEMATICS
(2021)
Article
Mathematics, Applied
T. T. A. Nghia, D. T. Pham, T. T. T. Tran
Summary: This paper explores the connection between the positive definiteness of limiting coderivative and the local strong maximal monotonicity of set-valued mappings. The conjecture proposed in a previous study was disproved with a counterexample, but special cases where it holds true were identified. Additionally, a new property called nearly strong monotonicity was introduced, and it was shown that strong metric regularity of set-valued mappings can be achieved under the positive definiteness of limiting coderivative.
SET-VALUED AND VARIATIONAL ANALYSIS
(2021)
Article
Mathematics, Applied
Nikolaos S. Papageorgiou, Andrea Scapellato
Summary: This paper investigates a nonlinear eigenvalue problem with a weighted (p, q)-Laplacian and a superlinear reaction. The authors prove the global existence and multiplicity of solutions for lambda > 0, generate nodal solutions, and determine the topological properties of the solution set. They also establish the continuity properties of the solution multifunction.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2023)
Article
Mathematics, Applied
Xiaowei Xue, Chunmei Liao, Minghua Li, Chengwu Lu
Summary: This paper deals with sensitivity analysis for a parametric vector variational inequality problem in finite dimensional spaces using advanced tools in modern variational analysis and generalized differentiation. The study focuses on computing the coderivatives of the solution mapping and applying them to establish verifiable conditions for the Aubin property of the solution mapping.
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS
(2022)
Article
Mathematics
V. T. T. Duong, D. Q. Khai, N. M. Tri
Summary: The text discusses the regularity of weak solutions of the unstationary Navier-Stokes equations in a general domain and their relationship with kinetic energy. The study extends previous results and provides specific mathematical expressions to support the findings.
MATHEMATISCHE NACHRICHTEN
(2021)
Article
Mathematics, Applied
Eugene Bilokopytov
Summary: This paper focuses on vector lattices endowed with locally solid convergence structures, which may not be topological. The convergence is defined by the convergence to 0 on the positive cone. Several results on unbounded modification are generalized. Order convergence is characterized as the strongest locally solid convergence where monotone nets converge to their extremums. The partial characterization of sublattices is explored in terms of order convergence. The study also investigates the relationship between order continuity and uo continuity, and gives a characterization of uo convergence independently of order convergence. The paper concludes with results on positive operators, closure of regular sublattices, and an example of a regular sublattice with a non-regular closure.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Yuejiao Feng
Summary: This article discusses the regularity of weak solutions for a variational inequality problem involving a recently studied fourth-order parabolic operator. Internal regular estimate of weak solutions is first considered using a difference type test function. Then, the near edge regularity and global regularity of weak solutions are analyzed using the finite cover principle. By constructing a test function using a spatial difference operator, the regularity proof is completed despite the quadratic gradient of the weak solution not satisfying the conditions for a test function. The results indicate that the weak solution has a second order regularity and an L infinity(0, T; H2(ohm)) estimation independent of the lower order norm of the weak one.
Article
Mathematics, Applied
Eduardo Cuesta, Rodrigo Ponce
Summary: The study investigated the optimal regularity in terms of Holder continuity of linear and semi-linear abstract fractional differential equations in the framework of complex Banach spaces for providing a posteriori error estimates. The error can be bounded in terms of computable quantities, measured in the norm of Holder continuous and weighted Holder continuous functions, under certain assumptions.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Xiaodong Zhang, Junfeng Liu
Summary: This paper investigates a class of high-order fractional stochastic partial differential equations driven by fractional noise. The existence and uniqueness of the mild solution are proven, and the Holder continuity of the solution with respect to space and time variables is studied. Additionally, the existence and Gaussian-type estimates for the density of the solution are also demonstrated using Malliavin calculus techniques.
Article
Mathematics, Applied
Geunsu Choi, Mingu Jung, Sun Kwang Kim, Miguel Martin
Summary: This paper studies weak-star quasi norm attaining operators and proves that the set of such operators is dense in the space of bounded linear operators regardless of the choice of Banach spaces. It is also shown that weak-star quasi norm attaining operators have distinct properties from other types of norm attaining operators, although they may share some equivalent properties under certain conditions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maria Lorente, Francisco J. Martin-Reyes, Israel P. Rivera-Rios
Summary: In this paper, we provide quantitative one-sided estimates that recover the dependences in the classical setting. We estimate the one-sided maximal function in Lorentz spaces and demonstrate the applicability of the conjugation method for commutators in this context.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Fernando Cobos, Luz M. Fernandez-Cabrera
Summary: We provide a necessary and sufficient condition for the weak compactness of bilinear operators interpolated using the real method. However, this characterization does not hold for interpolated operators using the complex method.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ovgue Gurel Yilmaz, Sofiya Ostrovska, Mehmet Turan
Summary: The Lupas q-analogue Rn,q, the first q-version of the Bernstein polynomials, was originally proposed by A. Lupas in 1987 but gained popularity 20 years later when q-analogues of classical operators in approximation theory became a focus of intensive research. This work investigates the continuity of operators Rn,q with respect to the parameter q in both the strong operator topology and the uniform operator topology, considering both fixed and infinite n.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
M. Agranovsky, A. Koldobsky, D. Ryabogin, V. Yaskin
Summary: This article modifies the concept of polynomial integrability for even dimensions and proves that ellipsoids are the only convex infinitely smooth bodies satisfying this property.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Abel Komalovics, Lajos Molnar
Summary: In this paper, a parametric family of two-variable maps on positive cones of C*-algebras is defined and studied from various perspectives. The square roots of the values of these maps under a faithful tracial positive linear functional are considered as a family of potential distance measures. The study explores the problem of well-definedness and whether these distance measures are true metrics, and also provides some related trace characterizations. Several difficult open questions are formulated.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Frederic Bayart
Summary: The passage describes the construction of an operator on a separable Hilbert space that is 5-hypercyclic for all δ in the range (ε, 1) and is not 5-hypercyclic for all δ in the range (0, ε).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Helene Frankowska, Nikolai P. Osmolovskii
Summary: This paper investigates second-order optimality conditions for the minimization problem of a C2 function f on a general set K in a Banach space X. Both necessary and sufficient conditions are discussed, with the sufficiency condition requiring additional assumptions. The paper demonstrates the validity of these assumptions for the case when the set K is an intersection of sets described by smooth inequalities and equalities, such as in mathematical programming problems. The novelty of the approach lies in the arbitrary nature of the set K and the straightforward proofs.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ole Fredrik Brevig, Kristian Seip
Summary: This paper studies the Hankel operator on the Hardy space and discusses its minimal and maximal norms, as well as the relationship between the maximal norm and the properties of the function.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Alexander Meskhi
Summary: Rubio de Francia's extrapolation theorem is established for new weighted grand Morrey spaces Mp),lambda,theta w (X) with weights w beyond the Muckenhoupt Ap classes. This result implies the one-weight inequality for operators of Harmonic Analysis in these spaces for appropriate weights. The necessary conditions for the boundedness of the Hardy-Littlewood maximal operator and the Hilbert transform in these spaces are also obtained. Some structural properties of new weighted grand Morrey spaces are investigated. Problems are studied in the case when operators and spaces are defined on spaces of homogeneous type.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maud Szusterman
Summary: In this work, the necessary conditions on the structure of the boundary of a convex body K to satisfy all inequalities are investigated. A new solution for the 3-dimensional case is obtained in particular.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Rami Ayoush, Michal Wojciechowski
Summary: In this article, lower bounds for the lower Hausdorff dimension of finite measures are provided under certain restrictions on their quaternionic spherical harmonics expansions. This estimate is analogous to a result previously obtained by the authors for complex spheres.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
F. G. Abdullayev, V. V. Savchuk
Summary: This paper investigates the convergence and theorem proof of the Takenaka-Malmquist system and Fejer-type operator on the unit circle, and provides relevant results on the class of holomorphic functions representable by Cauchy-type integrals with bounded densities.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Sofiya Ostrovska, Mikhail I. Ostrovskii
Summary: This work aims to establish new results on the structure of transportation cost spaces. The main outcome of this paper states that if a metric space X contains an isometric copy of L1 in its transportation cost space, then it also contains a 1-complemented isometric copy of $1.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Pilar Rueda, Enrique A. Sanchez Perez
Summary: We prove a factorization theorem for Lipschitz operators acting on certain subsets of metric spaces of measurable functions and with values on general metric spaces. Our results show how a Lipschitz operator can be extended to a subset of other metric space of measurable functions that satisfies the following optimality condition: it is the biggest metric space, formed by measurable functions, to which the operator can be extended preserving the Lipschitz constant. Also, we demonstrate the coarsest metric that can be given for a metric space in which an order bounded lattice-valued-Lipschitz map is defined, and provide concrete examples involving the relevant space L0(mu).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)