The Experts below are selected from a list of 252 Experts worldwide ranked by ideXlab platform
Michel Thera - One of the best experts on this subject based on the ideXlab platform.
-
ekeland s Inverse Function Theorem in graded frechet spaces revisited for multiFunctions
Journal of Mathematical Analysis and Applications, 2018Co-Authors: Van Ngai Huynh, Michel TheraAbstract:Abstract In this paper, we present some Inverse Function Theorems and implicit Function Theorems for set-valued mappings between Frechet spaces. The proof relies on Lebesgue's Dominated Convergence Theorem and on Ekeland's variational principle. An application to the existence of solutions of differential equations in Frechet spaces with non-smooth data is given.
-
Ekeland's Inverse Function Theorem in graded Fr{\'e}chet spaces revisited for multiFunctions
arXiv: Classical Analysis and ODEs, 2016Co-Authors: Van Ngai Huynh, Michel TheraAbstract:In this paper, we present some implicit Function Theorems for set-valued mappings between Frechet spaces. The proof relies on Lebesgue's Dominated Convergence Theorem and on Ekeland's variational principle. An application to the existence of solutions of differential equations in Frechet spaces with non-smooth data is given.
-
ekeland s Inverse Function Theorem in graded fr e chet spaces revisited for multiFunctions
arXiv: Classical Analysis and ODEs, 2016Co-Authors: Van Ngai Huynh, Michel TheraAbstract:In this paper, we present some implicit Function Theorems for set-valued mappings between Frechet spaces. The proof relies on Lebesgue's Dominated Convergence Theorem and on Ekeland's variational principle. An application to the existence of solutions of differential equations in Frechet spaces with non-smooth data is given.
Markus Poppenberg - One of the best experts on this subject based on the ideXlab platform.
-
an Inverse Function Theorem in sobolev spaces and applications to quasi linear schrodinger equations
Journal of Mathematical Analysis and Applications, 2001Co-Authors: Markus PoppenbergAbstract:Abstract A Nash–Moser type Inverse Function Theorem in Banach spaces with loss of derivatives is proved, and applications are given to singular quasi-linear Schrodinger equations like the superfluid film equation in plasma physics. Based on an implicit Function Theorem in Sobolev spaces, a linearization method is introduced for the local and global well-posedness of the Cauchy problem for nonlinear evolution equations. The technique compensates for a loss of derivatives in the linearized problem. This is illustrated by an application to strongly singular quasi-linear Schrodinger equations where the nonlinearities include derivatives of second order. The local well-posedness of the Cauchy problem is proved in Sobolev spaces for arbitrary space dimension without assuming smallness assumptions on the initial value. Here the linearized problem is solved using hyperbolic semigroup theory, including evolution systems.
-
an Inverse Function Theorem for frechet spaces satisfying a smoothing property and dn
Mathematische Nachrichten, 1999Co-Authors: Markus PoppenbergAbstract:Classical Inverse Function Theorems of Nash-Moser type are proved for Frechet spaces that admit smoothing operators as introduced by Nash. In this note an Inverse Function Theorem is proved for Frechet spaces which only have to satisfy the condition (DN) of Vogt and the smoothing property (SΩ)t; for instance, any Frechet-Hilbert space which is an (Ω)-space in standard form has property (SΩ)t. The main result of this paper generalizes a Theorem of Lojasiewicz and Zehnder. It can be applied to the space C∞(K) if the compact K ⊂ ℝN is the closure of its interior and subanalytic; different from classical results the boundary of K may have singularities like cusps. The growth assumptions on the mappings are formulated in terms of the weighted multiseminorms [ ]m,k introduced in this paper; nonlinear smooth partial differential operators on C∞(K) and their derivatives satisfy these formal assumptions.
-
Negative results on the Nash-Moser Theorem for Köthe sequence spaces and for spaces of ultradifferentiable Functions
Manuscripta Mathematica, 1996Co-Authors: Markus PoppenbergAbstract:Counterexamples to the Nash-Moser Inverse Function Theorem are given for Kothe sequence spaces extending a result of Lojasiewicz and Zehnder. As an application also negative results are obtained for spaces of ultradifferentiable Functions of Beurling type, in particular for the Gevrey classes.
-
A Smoothing Property for Fréchet Spaces
Journal of Functional Analysis, 1996Co-Authors: Markus PoppenbergAbstract:A smoothing property (SΩ)tfor Frechet spaces is introduced generalizing the classical concept of smoothing operators which are important in the proof of Nash–Moser Inverse Function Theorems. For Frechet–Hilbert spaces property (Ω) in standard form in the sense of D. Vogt is shown to be sufficient for (SΩ)t. For instance, the spaces E(K) of infinitely differentiable Functions in the sense of Whitney have property (SΩ)tfor an arbitrary compactK⊂Rn; applications to extensions of Whitney Functions with estimates are included. In a forthcoming paper, an Inverse Function Theorem will be proved for Frechet spaces with properties (SΩ)tand (DN); this applies to E(K) if the compactK=K⊂Rnis subanalytic.
Frédéric Rochon - One of the best experts on this subject based on the ideXlab platform.
-
Geometrically Finite Poincaré–Einstein Metrics
Communications in Mathematical Physics, 2020Co-Authors: Eric Bahuaud, Frédéric RochonAbstract:We construct new examples of Einstein metrics by perturbing the conformal infinity of geometrically finite hyperbolic metrics and by applying the Inverse Function Theorem in suitable weighted Hölder spaces.
-
Geometrically finite Poincar\'e-Einstein metrics
arXiv: Differential Geometry, 2019Co-Authors: Eric Bahuaud, Frédéric RochonAbstract:We construct new examples of Einstein metrics by perturbing the conformal infinity of geometrically finite hyperbolic metrics and by applying the Inverse Function Theorem in suitable weighted Holder spaces.
Van Ngai Huynh - One of the best experts on this subject based on the ideXlab platform.
-
ekeland s Inverse Function Theorem in graded frechet spaces revisited for multiFunctions
Journal of Mathematical Analysis and Applications, 2018Co-Authors: Van Ngai Huynh, Michel TheraAbstract:Abstract In this paper, we present some Inverse Function Theorems and implicit Function Theorems for set-valued mappings between Frechet spaces. The proof relies on Lebesgue's Dominated Convergence Theorem and on Ekeland's variational principle. An application to the existence of solutions of differential equations in Frechet spaces with non-smooth data is given.
-
ekeland s Inverse Function Theorem in graded fr e chet spaces revisited for multiFunctions
arXiv: Classical Analysis and ODEs, 2016Co-Authors: Van Ngai Huynh, Michel TheraAbstract:In this paper, we present some implicit Function Theorems for set-valued mappings between Frechet spaces. The proof relies on Lebesgue's Dominated Convergence Theorem and on Ekeland's variational principle. An application to the existence of solutions of differential equations in Frechet spaces with non-smooth data is given.
Javad Lavaei - One of the best experts on this subject based on the ideXlab platform.
-
CDC - Inverse Function Theorem for polynomial equations using semidefinite programming
2015 54th IEEE Conference on Decision and Control (CDC), 2015Co-Authors: Morteza Ashraphijuo, Ramtin Madani, Javad LavaeiAbstract:This paper is concerned with obtaining the Inverse of polynomial Functions using semidefinite programming (SDP). Given a polynomial Function and a nominal point at which the Jacobian of the Function is invertible, the Inverse Function Theorem states that the Inverse of the polynomial Function exists at a neighborhood of the nominal point. In this work, we show that this Inverse Function can be found locally using convex optimization. More precisely, we propose infinitely many SDPs, each of which finds the Inverse Function at a neighborhood of the nominal point. We also design a convex optimization to check the existence of an SDP problem that finds the Inverse of the polynomial Function at multiple nominal points and a neighborhood around each point. This makes it possible to identify an SDP problem (if any) that finds the Inverse Function over a large region. As an application, any system of polynomial equations can be solved by means of the proposed SDP problem whenever an approximate solution is available. The method developed in this work is numerically compared with Newton's method and the nuclear-norm technique.
-
Inverse Function Theorem for polynomial equations using semidefinite programming
2015 54th IEEE Conference on Decision and Control (CDC), 2015Co-Authors: Morteza Ashraphijuo, Ramtin Madani, Javad LavaeiAbstract:This paper is concerned with obtaining the Inverse of polynomial Functions using semidefinite programming (SDP). Given a polynomial Function and a nominal point at which the Jacobian of the Function is invertible, the Inverse Function Theorem states that the Inverse of the polynomial Function exists at a neighborhood of the nominal point. In this work, we show that this Inverse Function can be found locally using convex optimization. More precisely, we propose infinitely many SDPs, each of which finds the Inverse Function at a neighborhood of the nominal point. We also design a convex optimization to check the existence of an SDP problem that finds the Inverse of the polynomial Function at multiple nominal points and a neighborhood around each point. This makes it possible to identify an SDP problem (if any) that finds the Inverse Function over a large region. As an application, any system of polynomial equations can be solved by means of the proposed SDP problem whenever an approximate solution is available. The method developed in this work is numerically compared with Newton's method and the nuclear-norm technique.
