A5060326176- Geometric Analysis and Curvature Flows
- Advanced Differential Geometry Research
- Nonlinear Partial Differential Equations
- Advanced Mathematical Modeling in Engineering
- Advanced Harmonic Analysis Research
- Railway Systems and Energy Efficiency
- Elevator Systems and Control
- Cosmology and Gravitation Theories
- Contact Mechanics and Variational Inequalities
- Inertial Sensor and Navigation
- Electric and Hybrid Vehicle Technologies
- Dermatological and Skeletal Disorders
- Robotics and Sensor-Based Localization
- Advanced Mathematical Physics Problems
Babeș-Bolyai University
2020-2023
Obuda University
2020-2022
Building Research Institute
2022
Eötvös Loránd University
2021
We establish a Talenti-type comparison theorem for the Dirichlet problem associated with Poisson’s equation on complete noncompact Finsler manifolds having nonnegative Ricci curvature and Euclidean volume growth. The proof relies anisotropic symmetrization arguments leverages sharp isoperimetric inequality recently established by Manini [Preprint, arXiv:2212.05130, 2022 ]. In addition, we characterize rigidity of principle under additional assumption that reversibility constant manifold is...
Combining the sharp isoperimetric inequality established by Z. Balogh and A. Kristály [Math. Ann., in press, doi:10.1007/s00208-022-02380-1] with an anisotropic symmetrization argument, we establish Morrey–Sobolev inequalities on [Formula: see text]-dimensional Finsler manifolds having nonnegative text]-Ricci curvature. A byproduct of this method is a Hardy–Sobolev-type same geometric setting. As applications, using variational arguments, guarantee existence/multiplicity solutions for...
Abstract Given a complete non-compact Riemannian manifold ( M , g ) with certain curvature restrictions, we introduce an expansion condition concerning group of isometries G that characterizes the coerciveness in sense Skrzypczak and Tintarev (Arch Math 101(3): 259–268, 2013). Furthermore, under these conditions, compact Sobolev-type embeddings à la Berestycki-Lions are proved for full range admissible parameters (Sobolev, Moser-Trudinger Morrey). We also consider case Randers-type Finsler...
The paper is devoted to prove Allard-Michael-Simon-type $L^p$-Sobolev $(p>1)$ inequalities with explicit constants on Euclidean submanifolds of any codimension. Such contain, beside the Dirichlet $p$-energy, a term involving mean curvature submanifold. Our results require separate discussions for cases $p\geq 2$ and $1<p<2$, respectively; in particular, 2$, coefficient front $p$-energy asymptotically sharp codimension-free. argument based optimal mass transport theory it also provides an...
We present the isometry between 2-dimensional Funk model and Finsler-Poincaré disk. Then, we introduce Finslerian Poincaré upper half plane model, which turns out to be also isometrically equivalent previous models. As application, state gapless character of first eigenvalue for aforementioned three spaces.
We introduce a new interior-point algorithm for linear optimization, which follows the central path, but it approaches optimal solution through infeasible points.This method is similar to Roos's algorithm, was conceived in 2005, based on other search directions.
In this paper we study a Dirichlet-type differential inclusion involving the Finsler-Laplace operator on complete Finsler manifold. Depending positive $\lambda$ parameter of inclusion, establish non-existence, as well existence and multiplicity results by applying non-smooth variational methods. The main difficulties are given problem's highly nonlinear nature due to general Finslerian setting, nonsmooth context.
In this paper we study a Dirichlet-type differential inclusion involving the Finsler-Laplace operator defined on complete Finsler manifold. Depending positive $\lambda$ parameter of problem, establish non-existence, as well existence and multiplicity results by applying non-smooth variational methods. The article's significance is given synthesis context with highly nonlinear problem inherent in general Finslerian framework.
Let $(M,g)$ be an $n$-dimensional $(n\geq 3)$ compact Riemannian manifold with Ric$_{(M,g)}\geq (n-1)g$. If supports AB-type critical Sobolev inequality constants close to the optimal ones corresponding standard unit sphere $(\mathbb S^n,g_0)$, we prove that is topologically S^n,g_0)$. Moreover, on are precisely S^n,g_0)$ if and only isometric S^n,g_0)$; in particular, latter result answers a question of V.H. Nguyen.
Given a complete non-compact Riemannian manifold $(M,g)$ with certain curvature restrictions, we introduce an expansion condition concerning group of isometries $G$ that characterizes the coerciveness in sense Skrzypczak and Tintarev (Arch. Math., 2013). Furthermore, under these conditions, compact Sobolev-type embeddings \`a la Berestycki-Lions are proved for full range admissible parameters (Sobolev, Moser-Trudinger Morrey). We also consider case Randers-type Finsler manifolds finite...
We establish Hardy inequalities involving a weight function on complete, not necessarily reversible Finsler manifolds. prove that the superharmonicity of provides sufficient condition to obtain inequalities. Namely, if $\rho$ is nonnegative and $-\boldsymbol{\Delta} \rho \geq 0$ in weak sense, where $\boldsymbol{\Delta}$ Finsler-Laplace operator defined by $ \boldsymbol{\Delta} = \mathrm{div}(\boldsymbol{\nabla} \rho)$, then we generalization some Riemannian given D'Ambrosio Dipierro (Ann....
We propose a train rescheduling algorithm which applies standardized feature selection based on pairwise conflicts in order to serve as input for the reinforcement learning framework. implement an analytical method identifies and optimally solves every conflict arising between two trains, then we design corresponding observation space features most relevant information considering these conflicts. The data obtained this way translates actions context of test our preliminary model using...
We propose a train rescheduling algorithm which applies standardized feature selection based on pairwise conflicts in order to serve as input for the reinforcement learning framework. implement an analytical method identifies and optimally solves every conflict arising between two trains, then we design corresponding observation space features most relevant information considering these conflicts. The data obtained this way translates actions context of test our preliminary model using...
Combining the sharp isoperimetric inequality established by Z. Balogh and A. Krist\'aly [Math. Ann., in press, doi:10.1007/s00208-022-02380-1] with an anisotropic symmetrization argument, we establish Morrey-Sobolev inequalities on $n$-dimensional Finsler manifolds having nonnegative $n$-Ricci curvature. A byproduct of this method is a Hardy-Sobolev-type same geometric setting. As applications, using variational arguments, guarantee existence/multiplicity solutions for certain eigenvalue...