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Alessandro Carlotto - One of the best experts on this subject based on the ideXlab platform.
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inequivalent complexity criteria for Free Boundary minimal surfaces
Advances in Mathematics, 2020Co-Authors: Alessandro Carlotto, Giada FranzAbstract:Abstract We obtain a series of results in the global theory of Free Boundary minimal surfaces, which in particular provide a rather complete picture for the way different complexity criteria, such as area, topology and Morse index compare, beyond the regime where effective estimates are at disposal.
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index estimates for Free Boundary minimal hypersurfaces
Mathematische Annalen, 2018Co-Authors: Lucas Ambrozio, Alessandro Carlotto, Ben SharpAbstract:We show that the Morse index of a properly embedded Free Boundary minimal hypersurface in a strictly mean convex domain of the Euclidean space grows linearly with the dimension of its first relative homology group (which is at least as big as the number of its Boundary components, minus one). In ambient dimension three, this implies a lower bound for the index of a Free Boundary minimal surface which is linear both with respect to the genus and the number of Boundary components. Thereby, the compactness theorem by Fraser and Li implies a strong compactness theorem for the space of Free Boundary minimal surfaces with uniformly bounded Morse index inside a convex domain. Our estimates also imply that the examples constructed, in the unit ball, by Fraser–Schoen and Folha–Pacard–Zolotareva have arbitrarily large index. Extensions of our results to more general settings (including various classes of positively curved Riemannian manifolds and other convexity assumptions) are discussed.
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compactness analysis for Free Boundary minimal hypersurfaces
Calculus of Variations and Partial Differential Equations, 2018Co-Authors: Lucas Ambrozio, Alessandro Carlotto, Ben SharpAbstract:We investigate compactness phenomena involving Free Boundary minimal hypersurfaces in Riemannian manifolds of dimension less than eight. We provide natural geometric conditions that ensure strong one-sheeted graphical subsequential convergence, discuss the limit behaviour when multi-sheeted convergence happens and derive various consequences in terms of finiteness and topological control.
Giada Franz - One of the best experts on this subject based on the ideXlab platform.
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inequivalent complexity criteria for Free Boundary minimal surfaces
Advances in Mathematics, 2020Co-Authors: Alessandro Carlotto, Giada FranzAbstract:Abstract We obtain a series of results in the global theory of Free Boundary minimal surfaces, which in particular provide a rather complete picture for the way different complexity criteria, such as area, topology and Morse index compare, beyond the regime where effective estimates are at disposal.
Mingxin Wang - One of the best experts on this subject based on the ideXlab platform.
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spreading and vanishing in the diffusive prey predator model with a Free Boundary
Communications in Nonlinear Science and Numerical Simulation, 2015Co-Authors: Mingxin WangAbstract:Abstract This paper deals with the diffusive Lotka–Volterra type prey–predator model with a Free Boundary over a one dimensional habitat. This problem may be used to describe the interaction between indigenous species and invasive species and the spreading of such two species, with the Free Boundary representing the expanding front. Our main purpose is to study the spreading and vanishing phenomena and long time behaviors of prey and predator.
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the diffusive logistic equation with a Free Boundary and sign changing coefficient
Journal of Differential Equations, 2015Co-Authors: Mingxin WangAbstract:Abstract This short paper concerns a diffusive logistic equation with a Free Boundary and sign-changing coefficient, which is formulated to study the spread of an invasive species, where the Free Boundary represents the expanding front. A spreading–vanishing dichotomy is derived, namely the species either successfully spreads to the right-half-space as time t → ∞ and survives (persists) in the new environment, or it fails to establish itself and will extinct in the long run. The sharp criteria for spreading and vanishing are also obtained. When spreading happens, we estimate the asymptotic spreading speed of the Free Boundary.
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on some Free Boundary problems of the prey predator model
Journal of Differential Equations, 2014Co-Authors: Mingxin WangAbstract:Abstract In this paper we investigate some Free Boundary problems for the Lotka–Volterra type prey–predator model in one space dimension. The main objective is to understand the asymptotic behavior of the two species (prey and predator) spreading via a Free Boundary. We prove a spreading–vanishing dichotomy, namely the two species either successfully spread to the entire space as time t goes to infinity and survive in the new environment, or they fail to establish and die out in the long run. The long time behavior of solution and criteria for spreading and vanishing are also obtained. Finally, when spreading successfully, we provide an estimate to show that the spreading speed (if exists) cannot be faster than the minimal speed of traveling wavefront solutions for the prey–predator model on the whole real line without a Free Boundary.
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the diffusive logistic equation with a Free Boundary and sign changing coefficient
arXiv: Analysis of PDEs, 2014Co-Authors: Mingxin WangAbstract:This short paper concerns a diffusive logistic equation with the heterogeneous environment and a Free Boundary, which is formulated to study the spread of an invasive species, where the Free Boundary represents the expanding front. A spreading-vanishing dichotomy is derived, namely the species either successfully spreads to the right-half-space as time $t\to\infty$ and survives (persists) in the new environment, or it fails to establish and will extinct in the long run. The sharp criteria for spreading and vanishing is also obtained. When spreading happens, we estimate the asymptotic spreading speed of the Free Boundary.
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Free Boundary problems for a lotka volterra competition system
Journal of Dynamics and Differential Equations, 2014Co-Authors: Mingxin Wang, Jingfu ZhaoAbstract:In this paper we investigate two Free Boundary problems for a Lotka–Volterra type competition model in one space dimension. The main objective is to understand the asymptotic behavior of the two competing species spreading via a Free Boundary. We prove a spreading-vanishing dichotomy, namely the two species either successfully spread to the right-half-space as time \(t\) goes to infinity and survive in the new environment, or they fail to establish and die out in the long run. The long time behavior of the solutions and criteria for spreading and vanishing are also obtained. This paper is an improvement and extension of Guo and Wu (J Dyn Differ Equ 24:873–895, 2012).
Zhou Yang - One of the best experts on this subject based on the ideXlab platform.
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Free Boundary Problem Concerning Pricing Convertible Bond1
2016Co-Authors: Zhou YangAbstract:Abstract: In this paper we consider some behaviors of the optimal conver-sion boundaries (i.e., Free boundaries) of American-style convertible bond with finite horizon in some case. The bond’s holder may convert it into the stock of its issued firm at any time before maturity, and the firm may call it at any time before maturity. Its pricing model is a parabolic variational inequality, in which the fundamental variables are time and the stock price of the bond’s issuer. We achieve some properties of the Free Boundary, besides the existence and uniqueness of the solution of the variational inequality, such as: the monotonicity, the boundedness, smoothness and its starting point. More-over, we analyze the relationship between the Free Boundary and the pa-rameters in the problem, as well as, obtain the critical condition where the Free Boundary is a constant independent of time
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Free Boundary Problem Arising From Pricing Convertible Bond, Applicable Analysis
2016Co-Authors: Zhou YangAbstract:Abstract: In this paper we study the behaviors of the optimal convertible Boundary (i.e. Free Boundary) of a American-style convertible bond with finite horizon (i.e. parabolic case). We prove that the existence and the uniqueness of the strong solution of the problem, the Free Boundary is bounded and smooth. Moreover, we show the Free Boundary’s start point and consider when it is monotonic or non-monotonic
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Free Boundary problem concerning pricing convertible bond
Mathematical Methods in The Applied Sciences, 2011Co-Authors: Zhou YangAbstract:In this paper, we consider some behaviors of the optimal conversion boundaries (i.e. Free boundaries) of American-style convertible bond with finite horizon in some case. The bond's holder may convert it into the stock of its issued firm at any time before maturity, and the firm may call it at any time before maturity. Its pricing model is a parabolic variational inequality, in which the fundamental variables are time and the stock price of the bond's issuer. We achieve some properties of the Free Boundary, besides the existence and uniqueness of the solution of the variational inequality, such as: the monotonicity, the boundedness, smoothness and its starting point. Moreover, we analyze the relationship between the Free Boundary and the parameters in the problem, as well as, obtain the critical condition where the Free Boundary is a constant independent of time. Copyright © 2011 John Wiley & Sons, Ltd.
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a Free Boundary problem arising from pricing convertible bond
Applicable Analysis, 2010Co-Authors: Zhou YangAbstract:In this article we study the behaviours of the optimal conversion Boundary (i.e. Free Boundary) of an American-style convertible bond with finite horizon (i.e. parabolic case). We prove the existence and the uniqueness of the strong solution of the problem and the boundedness and smoothness of the Free Boundary. Moreover, we characterize the Free Boundary's start point and present two numerical results.
Diego R Moreira - One of the best experts on this subject based on the ideXlab platform.
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erratum to least supersolution approach to regularizing Free Boundary problems
Archive for Rational Mechanics and Analysis, 2009Co-Authors: Diego R MoreiraAbstract:The paper [2], Least supersolution approach to regularizing Free Boundary problems. Arch. Rational Mech. Anal. 191 (2009), no. 1, 97–141, deals with a class of regularizing elliptic Free Boundary problems that are models in combustion theory. More specifically, we study the limit Free Boundary problem arising from passing the limit as e → 0 of the following family of semilinear equations u = βe(u)F(∇u) in (SEe)
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least supersolution approach to regularizing Free Boundary problems
Archive for Rational Mechanics and Analysis, 2009Co-Authors: Diego R MoreiraAbstract:In this paper, we study a Free Boundary problem obtained as a limit as e → 0 to the following regularizing family of semilinear equations \({\Delta u = \beta_{\varepsilon}(u) F(\nabla u)}\) , where βe approximates the Dirac delta in the origin and F is a Lipschitz function bounded away from 0 and infinity. The least supersolution approach is used to construct solutions satisfying geometric properties of the level surfaces that are uniform in e. This allows to prove that the Free Boundary of a limit has the “right” weak geometry, in the measure theoretical sense. By the construction of some barriers with curvature, the classification of global profiles of the blow-up analysis is carried out and the limit functions are proven to be viscosity and pointwise solution (\({\mathcal{H}^{n-1}}\) almost everywhere) to a Free Boundary problem. Finally, the Free Boundary is proven to be a C1,α surface around \({\mathcal{H}^{n-1}}\) almost everywhere point.
