Article
Mathematics
Stefano Buccheri, Luigi Orsina, Augusto C. Ponce
Summary: This study proves that each Borel function V defined on an open subset Omega subset of R-N induces a decomposition, such that the functions satisfying certain conditions are almost zero everywhere in certain regions, and the existence of nonnegative supersolutions leads to nonnegativity of the associated quadratic form.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2022)
Article
Mathematics, Applied
Vladimir Rabinovich
Summary: The passage discusses the magnetic anisotropic Schrodinger operator in the presence of magnetic and electric fields, setting specific physical and boundary conditions, and studying the properties and characteristics of the related operators.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Jianxiong Wang
Summary: The main purpose of this article is to establish L-p Hardy's identities and inequalities for Dunkl operator on any finite balls and the entire space R-N, as well as Hardy's identities and inequalities on certain domains with distance function to the boundary partial derivative Omega. By using the notion of Bessel pairs, we extend Hardy's identities for classical gradients to Dunkl gradients and significantly improve many existing Hardy's inequalities for Dunkl operators.
ADVANCED NONLINEAR STUDIES
(2022)
Article
Mathematics, Applied
Tianyi Ren
Summary: In this work, we establish resolvent estimates for Schrodinger operators with potentials in Lebesgue spaces in the Euclidean setting. While the (L-2, L-p) estimates were previously derived by Blair-Sogge-Sire, we extend their results to other (L-p, L-q) estimates by incorporating ideas from Kwon-Lee's work on non-uniform resolvent estimates in Euclidean space.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Wencai Liu
Summary: In this paper, three rigidity theorems for discrete periodic Schrodinger operators in any dimension d≥3 are proven.
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
(2023)
Article
Mathematics
Peter D. Hislop, Robert Wolf
Summary: This paper proves the compactness of a restricted set of real-valued, compactly supported potentials, for which the corresponding Schrodinger operators have the same resonances, including multiplicities. The set of potentials is shown to be a compact subset in a specific topology, with discussions on extensions to Sobolev spaces for less regular potentials.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2021)
Article
Mathematics, Applied
Kleber Carrapatoso, Jean Dolbeault, Frederic Herau, Stephane Mischler, Clement Mouhot
Summary: We prove functional inequalities on vector fields u : R-d -> R-d when R-d is equipped with a bounded measure e(-phi) dx that satisfies a Poincare inequality, and study associated self-adjoint operators. The weighted Korn inequality compares the differential matrix Du, once projected orthogonally to certain finite-dimensional spaces, with its symmetric part D(s)u and, in an improved form of the inequality, an additional term del phi.u. We also consider Poincare-Korn inequalities for estimating a projection of u by D(s)u and zeroth-order versions of these inequalities obtained using the Witten-Laplace operator. The constants depend on geometric properties of the potential phi and the estimates are quantitative and constructive. These inequalities are motivated by kinetic theory and related with the Korn inequality (1906) in mechanics, which compares Du and D(s)u on a bounded domain.
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2022)
Article
Physics, Mathematical
Jan Derezinski, Oskar Grocholski
Summary: This article analyzes the Bessel operator in the momentum representation, which is the Schrodinger operator with a potential proportional to 1/x(2) on the half-line. The analysis reveals many similarities between this operator and Wilson's approach in quantum field theory, such as the need for a cutoff, the addition of counterterms, and the study of renormalization group flow with fixed points and limit cycles.
JOURNAL OF MATHEMATICAL PHYSICS
(2022)
Article
Mathematics
David Krejcirik, Tho Nguyen Duc
Summary: This article constructs pseudo modes of one-dimensional Dirac operators by analyzing the behavior of the complex-valued electromagnetic potential in the neighborhood of infinity, and achieves a systematic approach beyond the standard semiclassical setting. Furthermore, significant progress has been made in achieving optimal conditions and conclusions, as well as covering a wide range of previously inaccessible potentials.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Mathematics, Interdisciplinary Applications
Ibtehal Alazman, Mohamed Jleli, Bessem Samet
Summary: This paper investigates a Schrodinger equation with a time-fractional derivative in (0, infinity) x I, with I =] a, b]. The equation involves a singular Hardy potential of the form lambda/(x-a)(2), where the parameter lambda belongs to a certain range, and a nonlinearity of the form mu(x - a)(-rho)vertical bar u vertical bar(p), where rho >= 0. Necessary conditions for the existence of weak solutions are obtained using some a priori estimates.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Zahra Maleki Khouzani, Seyed Mahmoud Manjegani
Summary: This paper focuses on the study of the Young, Holder, and Heinz mean inequalities for a semi-finite von Neumann algebra M, and extends the results to tau-measurable operators. The paper obtains refinements of these inequalities for tau-measurable operators and presents several inequalities in the sense of majorization.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2022)
Article
Multidisciplinary Sciences
Ghada AlNemer, Mohammed Kenawy, Mohammed Zakarya, Clemente Cesarano, Haytham M. Rezk
Summary: This paper derives new fractional extensions of Hardy's type inequalities, and obtains corresponding reverse relations using conformable fractional calculus, from which classical integral inequalities can be deduced as special cases when α=1.
Article
Mathematics
Ahmed A. El-Deeb, Samer D. Makharesh, Sameh S. Askar, Jan Awrejcewicz
Summary: The primary goal of this research is to prove new Hardy-type backward difference -conformable dynamic inequalities on time scales by employing various mathematical techniques. The results extend and generalize existing knowledge in the field.
Article
Mathematics
Anna Canale
Summary: In this paper, we investigate Hardy type inequalities and their applications to evolution problems. Specifically, we focus on local and nonlocal weighted improved Hardy inequalities related to Kolmogorov operators perturbed by singular potentials. The class of weights considered is wide enough to encompass a range of scenarios. Our approach involves introducing a suitable vector-valued function and utilizing a generalized vector field method. The local estimates provide examples of potentials of this type and extend known results to the weighted case.
Article
Engineering, Multidisciplinary
Hany A. Atia, H. M. Abu-Donia, F. Mahmoud Ellaithy
Summary: This paper explores the separability of a non-linear Schrodinger operator and provides the necessary conditions for separability in the specified space, along with establishing suitable coercive inequalities.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Applied
Veronica Felli, Alberto Ferrero
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2020)
Article
Mathematics, Applied
Veronica Felli, Alberto Ferrero
Article
Mathematics, Applied
Veronica Felli, Benedetta Noris, Roberto Ognibene
Summary: This work investigates the homogeneous Neumann eigenvalue problem for the Laplacian on a bounded Lipschitz domain and a singular perturbation of it. The study reveals that the sharp asymptotic behavior of the perturbed eigenvalue is influenced by the Sobolev capacity of the subset where the perturbed eigenfunction vanishes when converging to a simple eigenvalue of the limit Neumann problem. Additionally, a focus is placed on the case of Dirichlet boundary conditions imposed on a subset scaling to a point, and the vanishing order of the Sobolev capacity of such shrinking Dirichlet boundary portion is determined through blow-up analysis for the capacitary potentials.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics
Alberto Boscaggin, Walter Dambrosio, Guglielmo Feltrin, Susanna Terracini
Summary: This paper proves the existence of half-entire parabolic solutions for a specific equation, asymptotic to a prescribed central configuration. The proof relies on a perturbative argument and an appropriate formulation of the problem in a suitable functional space. Applications to various problems in Celestial Mechanics are provided.
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY
(2021)
Article
Mathematics, Applied
Vivina Barutello, Gian Marco Canneori, Susanna Terracini
Summary: This paper proves symbolic dynamics for an Ncentre problem at slightly negative energy and explains the characteristics of the potentials V-j as well as the proof method. The lack of regularization of singularities poses a major difficulty, but the proof is achieved through a broken geodesics argument.
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2021)
Review
Endocrinology & Metabolism
C. Campana, F. Nista, L. Castelletti, M. Caputo, E. Lavezzi, P. Marzullo, A. Ferrero, G. Gaggero, F. R. Canevari, D. C. Rossi, G. Zona, A. Lania, D. Ferone, F. Gatto
Summary: This multicenter retrospective study investigated the rare occurrence of parasellar ectopic pituitary adenomas (pEPAs) and found heterogeneity in terms of clinical and radiological presentations and hormone secretion. Some cases showed radiological evidence of bone invasion. A systematic review of the literature indicated that medical therapy can be effective in managing hydroxy-secreting pEPAs. These findings highlight the importance of considering pEPAs in the differential diagnosis of parasellar lesions.
JOURNAL OF ENDOCRINOLOGICAL INVESTIGATION
(2022)
Article
Mathematics
Alessandra De Luca, Veronica Felli, Stefano Vita
Summary: We study the local asymptotics of solutions to fractional elliptic equations at boundary points under outer homogeneous Dirichlet boundary condition. Our analysis is based on a blow-up procedure involving Almgren-type monotonicity formulas, and it provides a classification of all possible homogeneity degrees of limiting entire profiles. As a consequence, we establish a strong unique continuation principle from boundary points.
ADVANCES IN MATHEMATICS
(2022)
Article
Mathematics
Veronica Felli, Benedetta Noris, Roberto Ognibene
Summary: This article deals with eigenvalue problems for the Laplacian with varying mixed boundary conditions, where homogeneous Neumann conditions are imposed on a vanishing portion of the boundary and Dirichlet conditions are imposed on the complement. Through the study of an Almgren-type frequency function, upper and lower bounds of the eigenvalue variation are derived, along with sharp estimates in the case of a strictly star-shaped Neumann region.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Alberto Ferrero, Pier Domenico Lamberti
Summary: This paper investigates the stability properties of the spectrum of the classical Steklov problem under domain perturbation, finding conditions for spectral stability and showing their optimality. The convergence of eigenfunctions can be expressed in terms of the H-1 strong convergence.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Mathematics, Applied
Veronica Felli, Giovanni Siclari
Summary: In this paper, we derive local asymptotics of solutions to second order elliptic equations at the edge of a (N-1)-dimensional crack, with homogeneous Neumann boundary conditions prescribed on both sides of the crack. A combination of blow-up analysis and monotonicity arguments provides a classification of all possible asymptotic homogeneities of solutions at the crack's tip, together with a strong unique continuation principle.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Mathematics, Applied
Alberto Ferrero
Summary: The paper aims to compare two different approaches in modeling the deck of a suspension bridge: one treating it as a rectangular plate and the other considering it as a beam for vertical deflections and as a rod for torsional deformations. The beam-rod model is found to be more suitable for describing the behavior of the deck. The study suggests a possible strategy to improve the efficiency of the plate model by relaxing the isotropy condition.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2022)
Article
Mathematics, Applied
Veronica Felli, Giulio Romani
Summary: We study the singular perturbations of eigenvalues of the polyharmonic operator on bounded domains by removing small interior compact sets. We consider homogeneous Dirichlet and Navier conditions on the external boundary, while imposing homogeneous Dirichlet conditions on the boundary of the removed set. We develop a suitable notion of capacity and use it to describe the asymptotic behavior of perturbed simple eigenvalues in terms of the removed set's capacity and the respective normalized eigenfunction.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Automation & Control Systems
Alessandra De Luca, Veronica Felli, Giovanni Siclari
Summary: This article investigates the unique continuation properties and asymptotic behavior at boundary points for a class of elliptic equations involving the spectral fractional Laplacian. By studying a degenerate or singular equation on a cylinder with specific boundary conditions, the authors are able to classify the local asymptotic profiles at the edge where the transition between boundary conditions occurs. By analyzing the traces, they also deduce a strong unique continuation property for the nonlocal fractional equation.
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
(2023)
Article
Mathematics, Interdisciplinary Applications
Alessandra De Luca, Veronica Felli
Summary: In this work, an Almgren type monotonicity formula is developed for a class of elliptic equations in a domain with a crack, under certain conditions on the potentials. The study of the Almgren frequency function around a point on the edge of the crack involves approximation arguments using a sequence of regular sets. The finite limit of the Almgren frequency is shown to exist, allowing for blow-up analysis of scaled solutions and proving asymptotic expansions and strong unique continuation from the edge of the crack.
MATHEMATICS IN ENGINEERING
(2021)
Article
Mathematics, Applied
Vivina Barutello, Gian Marco Canneori, Susanna Terracini
Summary: The study focuses on analyzing finite time collision trajectories for a class of singular anisotropic homogeneous potentials, showing that the asymptotic configuration converges to a central configuration and that the local stable manifold coincides with that of the initial data of minimal collision arcs in a general setting. The proof makes use of the generalized Sundman's monotonicity formula.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2021)
