Holder Continuity Of Weak Solutions To Subelliptic Equations With Rough Coefficients
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Holder Continuity Of Weak Solutions To Subelliptic Equations With Rough Coefficients
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Author : Eric T. Sawyer
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2014-09-11
Holder Continuity Of Weak Solutions To Subelliptic Equations With Rough Coefficients written by Eric T. Sawyer and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Differential equations, Hypoelliptic categories.
Introduction Comparisons of conditions Proof of the general subellipticity theorem Reduction of the proofs of the rough diagonal extensions of Hormander's theorem Homogeneous spaces and subrepresentation inequalities Appendix Bibliography
Holder Continuity Of Weak Solutions To Subelliptic Equations With Rough Coefficients
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Author : Eric T. Sawyer
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Holder Continuity Of Weak Solutions To Subelliptic Equations With Rough Coefficients written by Eric T. Sawyer and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This mathematical monograph is a study of interior regularity of weak solutions of second order linear divergence form equations with degenerate ellipticity and rough coefficients. The authors show that solutions of large classes of subelliptic equations with bounded measurable coefficients are H lder continuous. They present two types of results f
Extended Abstracts 2021 2022
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Author : Duván Cardona
language : en
Publisher: Springer Nature
Release Date : 2024-02-28
Extended Abstracts 2021 2022 written by Duván Cardona and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-28 with Mathematics categories.
This volume presents modern developments in analysis, PDEs and geometric analysis by some of the leading worldwide experts, prominent junior and senior researchers who were invited to be part of the Ghent Analysis & PDE Center Methusalem Seminars from 2021 to 2022. The contributions are from the speakers of the Methusalem Colloquium, Methusalem Junior Seminar and Geometric Analysis Seminar. The volume has two main topics: 1. Analysis and PDEs. The volume presents recent results in fundamental problems for solving partial integro-differential equations in different settings such as Euclidean spaces, manifolds, Banach spaces, and many others. Discussions about the global and local solvability using micro-local and harmonic analysis methods, studies of new techniques and approaches arising from a physical perspective or the mathematical point of view have also been included. Several connected branches arising in this regard are shown. 2. Geometric analysis. The volume presents studies of modern techniques for elliptic and subelliptic PDEs that in recent times have been used to establish new results in differential geometry and differential topology. These topics involve the intrinsic research in microlocal analysis, geometric analysis, and harmonic analysis abroad. Different problems having relevant geometric information for different applications in mathematical physics and other problems of classification have been considered.
Local Boundedness Maximum Principles And Continuity Of Solutions To Infinitely Degenerate Elliptic Equations With Rough Coefficients
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Author : Lyudmila Korobenko
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-21
Local Boundedness Maximum Principles And Continuity Of Solutions To Infinitely Degenerate Elliptic Equations With Rough Coefficients written by Lyudmila Korobenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-21 with Education categories.
View the abstract: https://bookstore.ams.org/memo-269-1311/
Special Functions Partial Differential Equations And Harmonic Analysis
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Author : Constantine Georgakis
language : en
Publisher: Springer
Release Date : 2014-11-07
Special Functions Partial Differential Equations And Harmonic Analysis written by Constantine Georgakis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-07 with Mathematics categories.
This volume of papers presented at the conference in honor of Calixto P. Calderón by his friends, colleagues, and students is intended to make the mathematical community aware of his important scholarly and research contributions in contemporary Harmonic Analysis and Mathematical Models applied to Biology and Medicine, and to stimulate further research in the future in this area of pure and applied mathematics.
Harmonic Analysis Partial Differential Equations And Applications
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Author : Sagun Chanillo
language : en
Publisher: Birkhäuser
Release Date : 2017-02-20
Harmonic Analysis Partial Differential Equations And Applications written by Sagun Chanillo and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-20 with Mathematics categories.
This collection of articles and surveys is devoted to Harmonic Analysis, related Partial Differential Equations and Applications and in particular to the fields of research to which Richard L. Wheeden made profound contributions. The papers deal with Weighted Norm inequalities for classical operators like Singular integrals, fractional integrals and maximal functions that arise in Harmonic Analysis. Other papers deal with applications of Harmonic Analysis to Degenerate Elliptic equations, variational problems, Several Complex variables, Potential theory, free boundaries and boundary behavior of functions.
Tangential Boundary Stabilization Of Navier Stokes Equations
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Author : Viorel Barbu
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Tangential Boundary Stabilization Of Navier Stokes Equations written by Viorel Barbu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
In order to inject dissipation as to force local exponential stabilization of the steady-state solutions, an Optimal Control Problem (OCP) with a quadratic cost functional over an infinite time-horizon is introduced for the linearized N-S equations. As a result, the same Riccati-based, optimal boundary feedback controller which is obtained in the linearized OCP is then selected and implemented also on the full N-S system. For $d=3$, the OCP falls definitely outside the boundaries of established optimal control theory for parabolic systems with boundary controls, in that the combined index of unboundedness--between the unboundedness of the boundary control operator and the unboundedness of the penalization or observation operator--is strictly larger than $\tfrac{3}{2}$, as expressed in terms of fractional powers of the free-dynamics operator. In contrast, established (and rich) optimal control theory [L-T.2] of boundary control parabolic problems and corresponding algebraic Riccati theory requires a combined index of unboundedness strictly less than 1. An additional preliminary serious difficulty to overcome lies at the outset of the program, in establishing that the present highly non-standard OCP--with the aforementioned high level of unboundedness in control and observation operators and subject, moreover, to the additional constraint that the controllers be pointwise tangential--be non-empty; that is, it satisfies the so-called Finite Cost Condition [L-T.2].
Basic Global Relative Invariants For Nonlinear Differential Equations
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Author : Roger Chalkley
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Basic Global Relative Invariants For Nonlinear Differential Equations written by Roger Chalkley and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
The problem of deducing the basic relative invariants possessed by monic homogeneous linear differential equations of order $m$ was initiated in 1879 with Edmund Laguerre's success for the special case $m = 3$. It was solved in number 744 of the Memoirs of the AMS (March 2002), by a procedure that explicitly constructs, for any $m \geq3$, each of the $m - 2$ basic relative invariants. During that 123-year time span, only a few results were published about the basic relative invariants for other classes of ordinary differential equations. With respect to any fixed integer $\, m \geq 1$, the author begins by explicitly specifying the basic relative invariants for the class $\, \mathcal{C {m,2 $ that contains equations like $Q {m = 0$ in which $Q {m $ is a quadratic form in $y(z), \, \dots, \, y{(m) (z)$ having meromorphic coefficients written symmetrically and the coefficient of $\bigl( y{(m) (z) \bigr){2 $ is $1$.Then, in terms of any fixed positive integers $m$ and $n$, the author explicitly specifies the basic relative invariants for the class $\, \mathcal{C {m, n $ that contains equations like $H {m, n = 0$ in which $H {m, n $ is an $n$th-degree form in $y(z), \, \dots, \, y{(m) (z)$ having meromorphic coefficients written symmetrically and the coefficient of $\bigl( y{(m) (z) \bigr){n $ is $1$.These results enable the author to obtain the basic relative invariants for additional classes of ordinary differential equa
Newton S Method Applied To Two Quadratic Equations In Mathbb C 2 Viewed As A Global Dynamical System
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Author : John H. Hubbard
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Newton S Method Applied To Two Quadratic Equations In Mathbb C 2 Viewed As A Global Dynamical System written by John H. Hubbard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The authors study the Newton map $N:\mathbb{C}^2\rightarrow\mathbb{C}^2$ associated to two equations in two unknowns, as a dynamical system. They focus on the first non-trivial case: two simultaneous quadratics, to intersect two conics. In the first two chapters, the authors prove among other things: The Russakovksi-Shiffman measure does not change the points of indeterminancy. The lines joining pairs of roots are invariant, and the Julia set of the restriction of $N$ to such a line has under appropriate circumstances an invariant manifold, which shares features of a stable manifold and a center manifold. The main part of the article concerns the behavior of $N$ at infinity. To compactify $\mathbb{C}^2$ in such a way that $N$ extends to the compactification, the authors must take the projective limit of an infinite sequence of blow-ups. The simultaneous presence of points of indeterminancy and of critical curves forces the authors to define a new kind of blow-up: the Farey blow-up. This construction is studied in its own right in chapter 4, where they show among others that the real oriented blow-up of the Farey blow-up has a topological structure reminiscent of the invariant tori of the KAM theorem. They also show that the cohomology, completed under the intersection inner product, is naturally isomorphic to the classical Sobolev space of functions with square-integrable derivatives. In chapter 5 the authors apply these results to the mapping $N$ in a particular case, which they generalize in chapter 6 to the intersection of any two conics.
The Universal Kobayashi Hitchin Correspondence On Hermitian Manifolds
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Author : Martin Lübke
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
The Universal Kobayashi Hitchin Correspondence On Hermitian Manifolds written by Martin Lübke and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
We prove a very general Kobayashi-Hitchin correspondence on arbitrary compact Hermitian manifolds, and we discuss differential geometric properties of the corresponding moduli spaces. This correspondence refers to moduli spaces of ``universal holomorphic oriented pairs''. Most of the classical moduli problems in complex geometry (e. g. holomorphic bundles with reductive structure groups, holomorphic pairs, holomorphic Higgs pairs, Witten triples, arbitrary quiver moduli problems) are special cases of this universal classification problem. Our Kobayashi-Hitchin correspondence relates the complex geometric concept ``polystable oriented holomorphic pair'' to the existence of a reduction solving a generalized Hermitian-Einstein equation. The proof is based on the Uhlenbeck-Yau continuity method. Using ideas from Donaldson theory, we further introduce and investigate canonical Hermitian metrics on such moduli spaces. We discuss in detail remarkable classes of moduli spaces in the non-Kahlerian framework: Oriented holomorphic structures, Quot-spaces, oriented holomorphic pairs and oriented vortices, non-abelian Seiberg-Witten monopoles.