Fundamental Solutions and Local Solvability for Nonsmooth Hörmander's Operators

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Publisher :
ISBN 13 : 9781470441319
Total Pages : 79 pages
Book Rating : 4.4/5 (413 download)

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Book Synopsis Fundamental Solutions and Local Solvability for Nonsmooth Hörmander's Operators by : Marco Bramanti

Download or read book Fundamental Solutions and Local Solvability for Nonsmooth Hörmander's Operators written by Marco Bramanti and published by . This book was released on 2017 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider operators of the form L=\sum_{i=1}^{n}X_{i}^{2}+X_{0} in a bounded domain of \mathbb{R}^{p} where X_{0},X_{1},\ldots,X_{n} are nonsmooth Hörmander's vector fields of step r such that the highest order commutators are only Hölder continuous. Applying Levi's parametrix method the authors construct a local fundamental solution \gamma for L and provide growth estimates for \gamma and its first derivatives with respect to the vector fields. Requiring the existence of one more derivative of the coefficients the authors prove that \gamma also possesses second derivatives, and the.

Fundamental Solutions and Local Solvability for Nonsmooth Hörmander’s Operators

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Publisher : American Mathematical Soc.
ISBN 13 : 1470425599
Total Pages : 79 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Fundamental Solutions and Local Solvability for Nonsmooth Hörmander’s Operators by : Marco Bramanti

Download or read book Fundamental Solutions and Local Solvability for Nonsmooth Hörmander’s Operators written by Marco Bramanti and published by American Mathematical Soc.. This book was released on 2017-09-25 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider operators of the form in a bounded domain of where are nonsmooth Hörmander's vector fields of step such that the highest order commutators are only Hölder continuous. Applying Levi's parametrix method the authors construct a local fundamental solution for and provide growth estimates for and its first derivatives with respect to the vector fields. Requiring the existence of one more derivative of the coefficients the authors prove that also possesses second derivatives, and they deduce the local solvability of , constructing, by means of , a solution to with Hölder continuous . The authors also prove estimates on this solution.

Geometric Methods in PDE’s

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Publisher : Springer
ISBN 13 : 3319026666
Total Pages : 373 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Geometric Methods in PDE’s by : Giovanna Citti

Download or read book Geometric Methods in PDE’s written by Giovanna Citti and published by Springer. This book was released on 2015-10-31 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. In recent years, the geometric properties of linear and nonlinear second order PDEs of elliptic and parabolic type have been extensively studied by many outstanding researchers. This book collects contributions from a selected group of leading experts who took part in the INdAM meeting "Geometric methods in PDEs", on the occasion of the 70th birthday of Ermanno Lanconelli. They describe a number of new achievements and/or the state of the art in their discipline of research, providing readers an overview of recent progress and future research trends in PDEs. In particular, the volume collects significant results for sub-elliptic equations, potential theory and diffusion equations, with an emphasis on comparing different methodologies and on their implications for theory and applications.

An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields

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Publisher : Springer Science & Business Media
ISBN 13 : 3319020870
Total Pages : 150 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields by : Marco Bramanti

Download or read book An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields written by Marco Bramanti and published by Springer Science & Business Media. This book was released on 2013-11-20 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​Hörmander's operators are an important class of linear elliptic-parabolic degenerate partial differential operators with smooth coefficients, which have been intensively studied since the late 1960s and are still an active field of research. This text provides the reader with a general overview of the field, with its motivations and problems, some of its fundamental results, and some recent lines of development.

Hormander Operators

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Publisher : World Scientific
ISBN 13 : 9811261709
Total Pages : 722 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Hormander Operators by : Marco Bramanti

Download or read book Hormander Operators written by Marco Bramanti and published by World Scientific. This book was released on 2022-10-21 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hörmander operators are a class of linear second order partial differential operators with nonnegative characteristic form and smooth coefficients, which are usually degenerate elliptic-parabolic, but nevertheless hypoelliptic, that is highly regularizing. The study of these operators began with the 1967 fundamental paper by Lars Hörmander and is intimately connected to the geometry of vector fields.Motivations for the study of Hörmander operators come for instance from Kolmogorov-Fokker-Planck equations arising from modeling physical systems governed by stochastic equations and the geometric theory of several complex variables. The aim of this book is to give a systematic exposition of a relevant part of the theory of Hörmander operators and vector fields, together with the necessary background and prerequisites.The book is intended for self-study, or as a reference book, and can be useful to both younger and senior researchers, already working in this area or aiming to approach it.

Boundary Conditions and Subelliptic Estimates for Geometric Kramers-Fokker-Planck Operators on Manifolds with Boundaries

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Publisher : American Mathematical Soc.
ISBN 13 : 1470428024
Total Pages : 142 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Boundary Conditions and Subelliptic Estimates for Geometric Kramers-Fokker-Planck Operators on Manifolds with Boundaries by : Francis Nier

Download or read book Boundary Conditions and Subelliptic Estimates for Geometric Kramers-Fokker-Planck Operators on Manifolds with Boundaries written by Francis Nier and published by American Mathematical Soc.. This book was released on 2018-03-19 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article is concerned with the maximal accretive realizations of geometric Kramers-Fokker-Planck operators on manifolds with boundaries. A general class of boundary conditions is introduced which ensures the maximal accretivity and some global subelliptic estimates. Those estimates imply nice spectral properties as well as exponential decay properties for the associated semigroup. Admissible boundary conditions cover a wide range of applications for the usual scalar Kramer-Fokker-Planck equation or Bismut's hypoelliptic laplacian.

From Vertex Operator Algebras to Conformal Nets and Back

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Publisher : American Mathematical Soc.
ISBN 13 : 147042858X
Total Pages : 85 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis From Vertex Operator Algebras to Conformal Nets and Back by : Sebastiano Carpi

Download or read book From Vertex Operator Algebras to Conformal Nets and Back written by Sebastiano Carpi and published by American Mathematical Soc.. This book was released on 2018-08-09 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. They present a general procedure which associates to every strongly local vertex operator algebra V a conformal net AV acting on the Hilbert space completion of V and prove that the isomorphism class of AV does not depend on the choice of the scalar product on V. They show that the class of strongly local vertex operator algebras is closed under taking tensor products and unitary subalgebras and that, for every strongly local vertex operator algebra V, the map W↦AW gives a one-to-one correspondence between the unitary subalgebras W of V and the covariant subnets of AV.

Nonsmooth Differential Geometry–An Approach Tailored for Spaces with Ricci Curvature Bounded from Below

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Publisher : American Mathematical Soc.
ISBN 13 : 1470427656
Total Pages : 161 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Nonsmooth Differential Geometry–An Approach Tailored for Spaces with Ricci Curvature Bounded from Below by : Nicola Gigli

Download or read book Nonsmooth Differential Geometry–An Approach Tailored for Spaces with Ricci Curvature Bounded from Below written by Nicola Gigli and published by American Mathematical Soc.. This book was released on 2018-02-23 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author discusses in which sense general metric measure spaces possess a first order differential structure. Building on this, spaces with Ricci curvature bounded from below a second order calculus can be developed, permitting the author to define Hessian, covariant/exterior derivatives and Ricci curvature.

Entire Solutions for Bistable Lattice Differential Equations with Obstacles

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Publisher : American Mathematical Soc.
ISBN 13 : 1470422018
Total Pages : 119 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Entire Solutions for Bistable Lattice Differential Equations with Obstacles by : Aaron Hoffman

Download or read book Entire Solutions for Bistable Lattice Differential Equations with Obstacles written by Aaron Hoffman and published by American Mathematical Soc.. This book was released on 2018-01-16 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions they show that wave-like solutions exist when obstacles (characterized by “holes”) are present in the lattice. Their work generalizes to the discrete spatial setting the results obtained in Berestycki, Hamel, and Matuno (2009) for the propagation of waves around obstacles in continuous spatial domains. The analysis hinges upon the development of sub and super-solutions for a class of discrete bistable reaction-diffusion problems and on a generalization of a classical result due to Aronson and Weinberger that concerns the spreading of localized disturbances.

On Non-Generic Finite Subgroups of Exceptional Algebraic Groups

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Publisher : American Mathematical Soc.
ISBN 13 : 1470428377
Total Pages : 156 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis On Non-Generic Finite Subgroups of Exceptional Algebraic Groups by : Alastair J. Litterick

Download or read book On Non-Generic Finite Subgroups of Exceptional Algebraic Groups written by Alastair J. Litterick and published by American Mathematical Soc.. This book was released on 2018-05-29 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in R

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Publisher : American Mathematical Soc.
ISBN 13 : 1470428016
Total Pages : 105 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in R by : Naiara V. de Paulo

Download or read book Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in R written by Naiara V. de Paulo and published by American Mathematical Soc.. This book was released on 2018-03-19 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article the authors study Hamiltonian flows associated to smooth functions R R restricted to energy levels close to critical levels. They assume the existence of a saddle-center equilibrium point in the zero energy level . The Hamiltonian function near is assumed to satisfy Moser's normal form and is assumed to lie in a strictly convex singular subset of . Then for all small, the energy level contains a subset near , diffeomorphic to the closed -ball, which admits a system of transversal sections , called a foliation. is a singular foliation of and contains two periodic orbits and as binding orbits. is the Lyapunoff orbit lying in the center manifold of , has Conley-Zehnder index and spans two rigid planes in . has Conley-Zehnder index and spans a one parameter family of planes in . A rigid cylinder connecting to completes . All regular leaves are transverse to the Hamiltonian vector field. The existence of a homoclinic orbit to in follows from this foliation.

Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori

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Publisher : American Mathematical Soc.
ISBN 13 : 1470428067
Total Pages : 118 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori by : Xiao Xiong

Download or read book Sobolev, Besov and Triebel-Lizorkin Spaces on Quantum Tori written by Xiao Xiong and published by American Mathematical Soc.. This book was released on 2018-03-19 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a noncommutative -torus (with a skew symmetric real -matrix). These spaces share many properties with their classical counterparts. The authors prove, among other basic properties, the lifting theorem for all these spaces and a Poincaré type inequality for Sobolev spaces.

The Maslov Index in Symplectic Banach Spaces

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Publisher : American Mathematical Soc.
ISBN 13 : 1470428008
Total Pages : 123 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Maslov Index in Symplectic Banach Spaces by : Bernhelm Booß-Bavnbek

Download or read book The Maslov Index in Symplectic Banach Spaces written by Bernhelm Booß-Bavnbek and published by American Mathematical Soc.. This book was released on 2018-03-19 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider a curve of Fredholm pairs of Lagrangian subspaces in a fixed Banach space with continuously varying weak symplectic structures. Assuming vanishing index, they obtain intrinsically a continuously varying splitting of the total Banach space into pairs of symplectic subspaces. Using such decompositions the authors define the Maslov index of the curve by symplectic reduction to the classical finite-dimensional case. The authors prove the transitivity of repeated symplectic reductions and obtain the invariance of the Maslov index under symplectic reduction while recovering all the standard properties of the Maslov index. As an application, the authors consider curves of elliptic operators which have varying principal symbol, varying maximal domain and are not necessarily of Dirac type. For this class of operator curves, the authors derive a desuspension spectral flow formula for varying well-posed boundary conditions on manifolds with boundary and obtain the splitting formula of the spectral flow on partitioned manifolds.

Crossed Products by Hecke Pairs

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Publisher : American Mathematical Soc.
ISBN 13 : 1470428091
Total Pages : 141 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Crossed Products by Hecke Pairs by : Rui Palma

Download or read book Crossed Products by Hecke Pairs written by Rui Palma and published by American Mathematical Soc.. This book was released on 2018-03-19 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author develops a theory of crossed products by actions of Hecke pairs , motivated by applications in non-abelian -duality. His approach gives back the usual crossed product construction whenever is a group and retains many of the aspects of crossed products by groups. The author starts by laying the -algebraic foundations of these crossed products by Hecke pairs and exploring their representation theory and then proceeds to study their different -completions. He establishes that his construction coincides with that of Laca, Larsen and Neshveyev whenever they are both definable and, as an application of his theory, he proves a Stone-von Neumann theorem for Hecke pairs which encompasses the work of an Huef, Kaliszewski and Raeburn.

Type II Blow Up Manifolds for the Energy Supercritical Semilinear Wave Equation

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Publisher : American Mathematical Soc.
ISBN 13 : 147042813X
Total Pages : 163 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Type II Blow Up Manifolds for the Energy Supercritical Semilinear Wave Equation by : Charles Collot

Download or read book Type II Blow Up Manifolds for the Energy Supercritical Semilinear Wave Equation written by Charles Collot and published by American Mathematical Soc.. This book was released on 2018-03-19 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our analysis adapts the robust energy method developed for the study of energy critical bubbles by Merle-Rapha¨el-Rodnianski, Rapha¨el-Rodnianski and Rapha¨el- Schweyer, the study of this issue for the supercritical semilinear heat equation done by Herrero-Vel´azquez, Matano-Merle and Mizoguchi, and the analogous result for the energy supercritical Schr¨odinger equation by Merle-Rapha¨el-Rodnianski.

Szegő Kernel Asymptotics for High Power of CR Line Bundles and Kodaira Embedding Theorems on CR Manifolds

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Publisher : American Mathematical Soc.
ISBN 13 : 1470441012
Total Pages : 140 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Szegő Kernel Asymptotics for High Power of CR Line Bundles and Kodaira Embedding Theorems on CR Manifolds by : Chin-Yu Hsiao

Download or read book Szegő Kernel Asymptotics for High Power of CR Line Bundles and Kodaira Embedding Theorems on CR Manifolds written by Chin-Yu Hsiao and published by American Mathematical Soc.. This book was released on 2018-08-09 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let X be an abstract not necessarily compact orientable CR manifold of dimension 2n−1, n⩾2, and let Lk be the k-th tensor power of a CR complex line bundle L over X. Given q∈{0,1,…,n−1}, let □(q)b,k be the Gaffney extension of Kohn Laplacian for (0,q) forms with values in Lk. For λ≥0, let Π(q)k,≤λ:=E((−∞,λ]), where E denotes the spectral measure of □(q)b,k. In this work, the author proves that Π(q)k,≤k−N0F∗k, FkΠ(q)k,≤k−N0F∗k, N0≥1, admit asymptotic expansions with respect to k on the non-degenerate part of the characteristic manifold of □(q)b,k, where Fk is some kind of microlocal cut-off function. Moreover, we show that FkΠ(q)k,≤0F∗k admits a full asymptotic expansion with respect to k if □(q)b,k has small spectral gap property with respect to Fk and Π(q)k,≤0 is k-negligible away the diagonal with respect to Fk. By using these asymptotics, the authors establish almost Kodaira embedding theorems on CR manifolds and Kodaira embedding theorems on CR manifolds with transversal CR S1 action.

Holomorphic Automorphic Forms and Cohomology

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Publisher : American Mathematical Soc.
ISBN 13 : 1470428555
Total Pages : 167 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Holomorphic Automorphic Forms and Cohomology by : Roelof Bruggeman

Download or read book Holomorphic Automorphic Forms and Cohomology written by Roelof Bruggeman and published by American Mathematical Soc.. This book was released on 2018-05-29 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: