Article
Mathematics, Applied
Ali H. Alkhaldi, Meraj Ali Khan, Shyamal Kumar Hui, Pradip Mandal
Summary: The objective of this paper is to study the inequality for Ricci curvature of a semi-slant warped product submanifold and discuss the equality case. Physical applications of these inequalities are provided, and the relationship between the base manifold and a sphere with constant sectional curvature is also discussed.
Article
Mathematics, Applied
Suchismita Patra, V. V. K. Srinivas Kumar
Summary: In this paper, a numerical scheme combining an improved minimax method and Newton's method is presented for finding multiple solutions of p-area problems. The theoretical convergence result, the convergence of finite element based solutions, and the instability analysis of unstable solutions through local minimax characterizations are discussed. Numerical experiments are also conducted to demonstrate the algorithm and theoretical results.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics
Mingzheng Sun, Jiabao Su, Leiga Zhao
Summary: This paper investigates bifurcation results near the origin for the p-Laplacian equation, and then multiple solutions are obtained through a combination of perturbation methods and minimax methods in critical groups.
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS
(2021)
Article
Mathematics
Akram Ali, Jae Won Lee, Ali H. Alkhaldi
Summary: The goal of this paper is to prove new upper bounds for the first positive eigenvalue of the p-Laplacian operator in terms of the mean curvature and constant sectional curvature on Riemannian manifolds. In particular, we provide various estimates of the first eigenvalue of the p-Laplacian operator on closed orientate n-dimensional Lagrangian submanifolds in a complex space form M-n(4 epsilon) with constant holomorphic sectional curvature 4 epsilon. As applications of our main theorem, we generalize the Reilly-inequality for the Laplacian to the p-Laplacian for a Lagrangian submanifold in a complex Euclidean space and complex projective space for epsilon = 0 and epsilon = 1, respectively.
INTERNATIONAL JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics, Applied
Wei Xi Li, Chao Jiang Xu
Summary: Based on condition (Ψ), we establish the local subellipticity of a system of complex vector fields related to the semi-classical Witten Laplacian.
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
(2021)
Article
Mathematics, Applied
Nobuyuki Kato, Masashi Misawa, Yoshihiko Yamaura
Summary: In this paper, the regularity of a parabolic p-Laplacian system (p > 2) is studied using the discrete Morse flow method, known as a way to approximate solutions to parabolic partial differential equations. The approximate solution is constructed from a sequence of minimizers of variational functionals, with Euler-Lagrange equations being the time-discretized p-Laplacian system. The aim is to establish that regularity estimates for the approximate solution hold uniformly on two approximation parameters and demonstrate strong convergence.
ANNALI DI MATEMATICA PURA ED APPLICATA
(2021)
Article
Mathematics, Applied
Silvia Frassu, Antonio Iannizzotto
Summary: This study investigates a Dirichlet problem driven by the degenerate fractional p-Laplacian and involving a nonlinear reaction. The research shows that under certain conditions, there are five nontrivial solutions for the problem, including two positive solutions, two negative solutions, and one nodal solution.
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Stefano Buccheri, Tommaso Leonori, Julio D. Rossi
Summary: In this study, it is proven that the gradients of solutions to the Dirichlet problem for -Delta(p)u(p) = f, with f > 0, converge strongly to the gradient of the limit function as p tends to infinity in every L-q space with 1 <= q < infinity. The sharpness of this convergence is demonstrated with a simple 1-dimensional example showing no convergence in L-infinity. Additionally, the same strong convergence is obtained within the support of nonnegative f, and similar results hold true for the eigenvalue problem for a certain class of domains, such as balls or stadiums.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Nadia Alluhaibi, Akram Ali
Summary: This approach provides new upper bounds for the first positive eigenvalue of the p-Laplacian operator using mean and constant sectional curvatures on Riemannian manifolds. It also offers estimates for the first nonzero eigenvalue of the p-Laplacian operator on closed orientated totally real submanifolds in a generalized complex space form, and generalizes the Reilly inequality to the p-Laplacian for totally real submanifolds in complex projective space and complex Euclidean space.
RICERCHE DI MATEMATICA
(2021)
Article
Mathematics
Richard Hind, Costantino Medori, Adriano Tomassini
Summary: An almost p-Kahler manifold is a triple (M, J, Omega) where (M, J) is an almost complex manifold of real dimension 2n and Omega is a closed real transverse (p, p)-form on (M, J) where 1 <= p <= n. When J is integrable, almost p-Kahler manifolds are called p-Kahler manifolds. We construct families of almost p-Kahler structures (J(t), Omega(t)) on C-3, C-4, and on the real torus T-6, arising as deformations of Kahler structures (J(0), g(0), omega(0)), such that the almost complex structures Jt cannot be locally compatible with any symplectic form for t not equal 0. Furthermore, examples of special compact nilmanifolds with and without almost p-Kahler structures are presented.
JOURNAL OF GEOMETRIC ANALYSIS
(2023)
Article
Mathematics
Morris Brooks, Giacomo Di Gesu
Summary: The study investigates stochastic quantization of a quartic double-well energy functional and derives optimal asymptotics for the exponentially small splitting of the ground state energy in the semiclassical regime. The results demonstrate that the L-2 spectral gap of the one-dimensional stochastic Allen-Cahn equation in finite volume satisfies a Kramers-type formula in the limit of vanishing noise, with tunneling estimates being uniform in dimension. Key estimates show that the constant separating two exponentially small eigenvalues from the rest of the spectrum can be independent of dimension.
JOURNAL OF FUNCTIONAL ANALYSIS
(2021)
Article
Mathematics, Applied
Benjamin Steinberg
Summary: We provide a concise proof for the contractibility of the orbit space of the p-subgroup complex of a finite group, employing Brown-Forman discrete Morse theory. This result was first conjectured by Webb and later proved by Symonds.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Mathematics, Applied
Weiqiang Zhang, Jiabin Zuo, Peihao Zhao
Summary: This article deals with a fractional p-Laplacian problem on a bounded domain Omega, and using variational arguments and Morse theory, three nontrivial solutions are obtained.
JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS
(2022)
Article
Mathematics
Mouhamed Moustapha Fall, Pierre Aime Feulefack, Remi Yvant Temgoua, Tobias Weth
Summary: In this work, an estimate of the Morse index of radially symmetric sign changing bounded weak solutions to the semilinear fractional Dirichlet problem is provided. The results show that different Morse index lower limits exist for solutions with different values of s.
ADVANCES IN MATHEMATICS
(2021)
Article
Mathematics
Roberto Mossa
Summary: This paper explores the property of Kahler manifolds satisfying the Delta-property, showing that manifolds with this property are complex space forms.
ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG
(2021)
