The Experts below are selected from a list of 30528 Experts worldwide ranked by ideXlab platform
Yu Yuan - One of the best experts on this subject based on the ideXlab platform.
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Regularity for convex viscosity solutions of special Lagrangian Equation
arXiv: Analysis of PDEs, 2019Co-Authors: Jingyi Chen, Ravi Shankar, Yu YuanAbstract:We establish interior regularity for convex viscosity solutions of the special Lagrangian Equation. Our result states that all such solutions are real analytic in the interior of the domain.
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Hessian estimates for special Lagrangian Equations with critical and supercritical phases in general dimensions
American Journal of Mathematics, 2014Co-Authors: Dake Wang, Yu YuanAbstract:We derive a priori interior Hessian estimates for special Lagrangian Equation with critical and supercritical phases in general higher dimensions. Our unified approach leads to sharper estimates even for the previously known three dimensional and convex solution cases.
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Hessian estimates for the sigma-2 Equationin dimension 3
Communications on Pure and Applied Mathematics, 2009Co-Authors: Micah Warren, Yu YuanAbstract:We derive a priori interior Hessian estimates for the special Lagrangian Equation � 2 D1 in dimension3. c � 2008 Wiley Periodicals, Inc.
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Hessian and gradient estimates for three dimensional special Lagrangian Equations with large phase
arXiv: Analysis of PDEs, 2008Co-Authors: Micah Warren, Yu YuanAbstract:We derive a priori interior Hessian and gradient estimates for special Lagrangian Equation of phase at least a critical value in dimension three.
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Hessian estimates for the sigma-2 Equation in dimension three
arXiv: Analysis of PDEs, 2007Co-Authors: Micah Warren, Yu YuanAbstract:We derive a priori interior Hessian estimates for the special Lagrangian Equation $\sigma_{2}=1$ in dimension three.
Jake P. Solomon - One of the best experts on this subject based on the ideXlab platform.
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Geodesics of positive Lagrangians from special Lagrangians with boundary
arXiv: Symplectic Geometry, 2020Co-Authors: Jake P. Solomon, Amitai M. YuvalAbstract:Geodesics in the space of positive Lagrangian submanifolds are solutions of a fully non-linear degenerate elliptic PDE. We show that a geodesic segment in the space of positive Lagrangians corresponds to a one parameter family of special Lagrangian cylinders, called the cylindrical transform. The boundaries of the cylinders are contained in the positive Lagrangians at the ends of the geodesic. The special Lagrangian Equation with positive Lagrangian boundary conditions is elliptic and the solution space is a smooth manifold, which is one dimensional in the case of cylinders. A geodesic can be recovered from its cylindrical transform by solving the Dirichlet problem for the Laplace operator on each cylinder. Using the cylindrical transform, we show the space of pairs of positive Lagrangian spheres connected by a geodesic is open. Thus, we obtain the first examples of strong solutions to the geodesic Equation in arbitrary dimension not invariant under isometries. In fact, the solutions we obtain are smooth away from a finite set of points.
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The degenerate special Lagrangian Equation
Advances in Mathematics, 2017Co-Authors: Yanir A. Rubinstein, Jake P. SolomonAbstract:Abstract This article introduces the degenerate special Lagrangian Equation (DSL) and develops the basic analytic tools to construct and study its solutions. The DSL governs geodesics in the space of positive graph Lagrangians in C n . Existence of geodesics in the space of positive Lagrangians is an important step in a program for proving existence and uniqueness of special Lagrangians. Moreover, it would imply certain cases of the strong Arnold conjecture from Hamiltonian dynamics. We show the DSL is degenerate elliptic. We introduce a space–time Lagrangian angle for one-parameter families of graph Lagrangians, and construct its regularized lift. The superlevel sets of the regularized lift define subEquations for the DSL in the sense of Harvey–Lawson. We extend the existence theory of Harvey–Lawson for subEquations to the setting of domains with corners, and thus obtain solutions to the Dirichlet problem for the DSL in all branches. Moreover, we introduce the calibration measure, which plays a role similar to that of the Monge–Ampere measure in convex and complex geometry. The existence of this measure and regularity estimates allow us to prove that the solutions we obtain in the outer branches of the DSL have a well-defined length in the space of positive Lagrangians.
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The degenerate special Lagrangian Equation
2015Co-Authors: Jake P. SolomonAbstract:The degenerate special Lagrangian Equation governs geodesics in the space of positive Lagrangians. Existence of such geodesics has implications for uniqueness and existence of special Lagrangians. It also yields lower bounds on the cardinality of Lagrangian intersec- tions related to the strong Arnold conjecture. An overview of what is known about the existence problem will be given. The talk is based on joint work with A. Yuval and with Y. Rubinstein.
Yumei Zou - One of the best experts on this subject based on the ideXlab platform.
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A relationship between linear stability and index of oscillations for Lagrangian Equation at higher order zones
Nonlinear Analysis: Real World Applications, 2019Co-Authors: Feng Wang, Yumei ZouAbstract:Abstract We solve some connections between the linear stability properties of oscillations and the corresponding topological degree. A sufficient and necessary condition for linear stability based on this idea is obtained at higher order zones. Moreover, this condition combined with eigenvalue theory is used to find some new results on the existence, uniqueness and linear stability of Lagrangian Equation under the higher order nonuniform nonresonance conditions.
Micah Warren - One of the best experts on this subject based on the ideXlab platform.
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Hessian estimates for the sigma-2 Equationin dimension 3
Communications on Pure and Applied Mathematics, 2009Co-Authors: Micah Warren, Yu YuanAbstract:We derive a priori interior Hessian estimates for the special Lagrangian Equation � 2 D1 in dimension3. c � 2008 Wiley Periodicals, Inc.
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Hessian and gradient estimates for three dimensional special Lagrangian Equations with large phase
arXiv: Analysis of PDEs, 2008Co-Authors: Micah Warren, Yu YuanAbstract:We derive a priori interior Hessian and gradient estimates for special Lagrangian Equation of phase at least a critical value in dimension three.
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Hessian estimates for the sigma-2 Equation in dimension three
arXiv: Analysis of PDEs, 2007Co-Authors: Micah Warren, Yu YuanAbstract:We derive a priori interior Hessian estimates for the special Lagrangian Equation $\sigma_{2}=1$ in dimension three.
Madhu Ramarakula - One of the best experts on this subject based on the ideXlab platform.
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An Efficient Uplink Power Control Algorithm for LTE-Advanced Relay Networks to Improve Coverage Area
Wireless Personal Communications, 2019Co-Authors: Madhu RamarakulaAbstract:Power and spectrum are limited resource, so always we needed efficient control techniques to handle them in every generation. In this paper an efficient uplink power control algorithm is proposed for LTE-Advanced relay networks to improve coverage area. It is a co-operative power control method. It is developed using the utility function concept that belongs to economic theory. This algorithm is a distributed one, which is to be set up in mobile stations operating at 3GPP LTE or LTE-Advanced relay networks. In this the Lagrangian Equation is used to solve the utility function to achieve optimal power control in the network. The outage probability analysis is carried out for the coverage area determination. It is observed that the proposed algorithm improves the cell edge user performance by maintaining the defined power levels in every mobile, improves the base station coverage area and decreases the interference level in the network.
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An Efficient Uplink Power Control Algorithm for LTE-Advanced Relay Networks to Improve Coverage Area
Wireless Personal Communications, 2019Co-Authors: Madhu RamarakulaAbstract:Power and spectrum are limited resource, so always we needed efficient control techniques to handle them in every generation. In this paper an efficient uplink power control algorithm is proposed for LTE-Advanced relay networks to improve coverage area. It is a co-operative power control method. It is developed using the utility function concept that belongs to economic theory. This algorithm is a distributed one, which is to be set up in mobile stations operating at 3GPP LTE or LTE-Advanced relay networks. In this the Lagrangian Equation is used to solve the utility function to achieve optimal power control in the network. The outage probability analysis is carried out for the coverage area determination. It is observed that the proposed algorithm improves the cell edge user performance by maintaining the defined power levels in every mobile, improves the base station coverage area and decreases the interference level in the network.
