The Dirichlet Problem For Parabolic Operators With Singular Drift Terms

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The Dirichlet Problem for Parabolic Operators with Singular Drift Terms

Steve Hofmann,John L. Lewis
The Dirichlet Problem for Parabolic Operators with Singular Drift Terms Book PDF

Author : Steve Hofmann,John L. Lewis
Publisher : Unknown
Page : 113 pages
File Size : 42,8 Mb
Release : 2014-09-11
Category : Dirichlet problem
ISBN : 1470403129

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The Dirichlet Problem for Parabolic Operators with Singular Drift Terms by Steve Hofmann,John L. Lewis Pdf

The Dirichlet problem and parabolic measure Absolute continuity and the $L^p$ Dirichlet problem: Part 1 Absolute continuity and the $L^p$ Dirichlet problem: Part 2.

The Dirichlet Problem for Parabolic Operators with Singular Drift Terms

Steve Hofmann,John L. Lewis
The Dirichlet Problem for Parabolic Operators with Singular Drift Terms Book PDF

Author : Steve Hofmann,John L. Lewis
Publisher : American Mathematical Soc.
Page : 129 pages
File Size : 51,8 Mb
Release : 2001
Category : Dirichlet problem
ISBN : 9780821826843

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The Dirichlet Problem for Parabolic Operators with Singular Drift Terms by Steve Hofmann,John L. Lewis Pdf

This memoir considers the Dirichlet problem for parabolic operators in a half space with singular drift terms. Chapter I begins the study of a parabolic PDE modelled on the pullback of the heat equation in certain time varying domains considered by Lewis-Murray and Hofmann-Lewis. Chapter II obtains mutual absolute continuity of parabolic measure and Lebesgue measure on the boundary of this halfspace and also that the $L DEGREESq(R DEGREESn)$ Dirichlet problem for these PDEs has a solution when $q$ is large enough. Chapter III proves an analogue of a theorem of Fefferman, Kenig, and Pipher for certain parabolic PDEs with singular drift terms. Each of the chapters that comprise this memoir has its own numbering system and list

Smooth Molecular Decompositions of Functions and Singular Integral Operators

John E. Gilbert
Smooth Molecular Decompositions of Functions and Singular Integral Operators Book PDF

Author : John E. Gilbert
Publisher : American Mathematical Soc.
Page : 89 pages
File Size : 53,9 Mb
Release : 2002
Category : Decomposition
ISBN : 9780821827727

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Smooth Molecular Decompositions of Functions and Singular Integral Operators by John E. Gilbert Pdf

Under minimal assumptions on a function $\psi$ the authors obtain wavelet-type frames of the form $\psi_{j, k}(x) = r DEGREES{(1/2)n j} \psi(r DEGREESj x - sk), j \in \integer, k \in \integer DEGREESn, $ for some $r > 1$ and $s > 0$. This collection is shown to be a frame for a scale of Triebel-Lizorkin spaces (which includes Lebesgue, Sobolev and Hardy spaces) and the reproducing formula converges in norm as well as pointwise a.e. The construction follows from a characterization of those operators which are bounded on a space of smooth molecules. This characterization also allows us to decompose a broad range of singular integral operators in ter

Sub-Laplacians with Drift on Lie Groups of Polynomial Volume Growth

Georgios K. Alexopoulos
Sub Laplacians with Drift on Lie Groups of Polynomial Volume Growth Book PDF

Author : Georgios K. Alexopoulos
Publisher : American Mathematical Soc.
Page : 101 pages
File Size : 42,7 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821827642

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Sub-Laplacians with Drift on Lie Groups of Polynomial Volume Growth by Georgios K. Alexopoulos Pdf

We prove a parabolic Harnack inequality for a centered sub-Laplacian $L$ on a connected Lie group $G$ of polynomial volume growth by using ideas from Homogenisation theory and by adapting the method of Krylov and Safonov. We use this inequality to obtain a Taylor formula for the heat functions and thus we also obtain Harnack inequalities for their space and time derivatives. We characterise the harmonic functions which grow polynomially. We obtain Gaussian estimates for the heat kernel and estimates similar to the classical Berry-Esseen estimate. Finally, we study the associated Riesz transform operators. If $L$ is not centered, then we can conjugate $L$ by a convenient multiplicative function and obtain another centered sub-Laplacian $L_C$. Thus our results also extend to non-centered sub-Laplacians.

Singular Quasilinearity and Higher Eigenvalues

Victor Lenard Shapiro
Singular Quasilinearity and Higher Eigenvalues Book PDF

Author : Victor Lenard Shapiro
Publisher : American Mathematical Soc.
Page : 174 pages
File Size : 41,9 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821827178

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Singular Quasilinearity and Higher Eigenvalues by Victor Lenard Shapiro Pdf

This text is intended for graduate students and research mathematicians interested in partial differential equations. It covers quasilinear elliptic equations and quasilinear parabolic equations.

Approximation and Entropy Numbers of Volterra Operators with Application to Brownian Motion

Mikhail A. Lifshits,Mikhail Anatolʹevich Lifshit︠s︡,Werner Linde
Approximation and Entropy Numbers of Volterra Operators with Application to Brownian Motion Book PDF

Author : Mikhail A. Lifshits,Mikhail Anatolʹevich Lifshit︠s︡,Werner Linde
Publisher : American Mathematical Soc.
Page : 103 pages
File Size : 51,7 Mb
Release : 2002
Category : Brownian motion processes
ISBN : 9780821827918

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Approximation and Entropy Numbers of Volterra Operators with Application to Brownian Motion by Mikhail A. Lifshits,Mikhail Anatolʹevich Lifshit︠s︡,Werner Linde Pdf

This text considers a specific Volterra integral operator and investigates its degree of compactness in terms of properties of certain kernel functions. In particular, under certain optimal integrability conditions the entropy numbers $e_n(T_{\rho, \psi})$ satisfy $c_1\norm{\rho\psi}_r0$.

Elliptic Partial Differential Operators and Symplectic Algebra

William Norrie Everitt,L. Markus (Lawrence)
Elliptic Partial Differential Operators and Symplectic Algebra Book PDF

Author : William Norrie Everitt,L. Markus (Lawrence)
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 43,6 Mb
Release : 2003
Category : Elliptic operators
ISBN : 9780821832356

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Elliptic Partial Differential Operators and Symplectic Algebra by William Norrie Everitt,L. Markus (Lawrence) Pdf

This investigation introduces a new description and classification for the set of all self-adjoint operators (not just those defined by differential boundary conditions) which are generated by a linear elliptic partial differential expression $A(\mathbf{x}, D)=\sum_{0\, \leq\, \left s\right \, \leq\,2m}a_{s} (\mathbf{x})D DEGREES{s}\;\text{for all}\;\mathbf{x}\in\Omega$ in a region $\Omega$, with compact closure $\overline{\Omega}$ and $C DEGREES{\infty }$-smooth boundary $\partial\Omega$, in Euclidean space $\mathbb{E} DEGREES{r}$ $(r\geq2).$ The order $2m\geq2$ and the spatial dimensio

Basic Global Relative Invariants for Homogeneous Linear Differential Equations

Roger Chalkley
Basic Global Relative Invariants for Homogeneous Linear Differential Equations Book PDF

Author : Roger Chalkley
Publisher : American Mathematical Soc.
Page : 223 pages
File Size : 41,8 Mb
Release : 2002
Category : Differential equations, Linear
ISBN : 9780821827819

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Basic Global Relative Invariants for Homogeneous Linear Differential Equations by Roger Chalkley Pdf

Given any fixed integer $m \ge 3$, the author presents simple formulas for $m - 2$ algebraically independent polynomials over $\mathbb{Q}$ having the remarkable property, with respect to transformations of homogeneous linear differential equations of order $m$, that each polynomial is both a semi-invariant of the first kind (with respect to changes of the dependent variable) and a semi-invariant of the second kind (with respect to changes of the independent variable). These relative invariants are suitable for global studies in several different contexts and do not require Laguerre-Forsyth reductions for their evaluation. In contrast, all of the general formulas for basic relative invariants that have been proposed by other researchers during the last 113 years are merely local ones that are either much too complicated or require a Laguerre-Forsyth reduction for each evaluation.

Spectral Decomposition of a Covering of $GL(r)$: the Borel case

Heng Sun
Spectral Decomposition of a Covering of GL r the Borel case Book PDF

Author : Heng Sun
Publisher : American Mathematical Soc.
Page : 79 pages
File Size : 40,6 Mb
Release : 2002
Category : Borel sets
ISBN : 9780821827758

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Spectral Decomposition of a Covering of $GL(r)$: the Borel case by Heng Sun Pdf

Let $F$ be a number field and ${\bf A}$ the ring of adeles over $F$. Suppose $\overline{G({\bf A})}$ is a metaplectic cover of $G({\bf A})=GL(r, {\bf A})$ which is given by the $n$-th Hilbert symbol on ${\bf A}$

$q$-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions

Douglas Bowman
q Difference Operators Orthogonal Polynomials and Symmetric Expansions Book PDF

Author : Douglas Bowman
Publisher : American Mathematical Soc.
Page : 73 pages
File Size : 52,9 Mb
Release : 2002
Category : Difference operators
ISBN : 9780821827741

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$q$-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions by Douglas Bowman Pdf

The author explores ramifications and extensions of a $q$-difference operator method first used by L.J. Rogers for deriving relationships between special functions involving certain fundamental $q$-symmetric polynomials. In special cases these symmetric polynomials reduce to well-known classes of orthogonal polynomials. A number of basic properties of these polynomials follow from this approach. This leads naturally to the evaluation of the Askey-Wilson integral and generalizations. Expansions of certain generalized basic hypergeometric functions in terms of the symmetric polynomials are also found. This provides a quick route to understanding the group structure generated by iterating the two-term transformations of these functions. Some infrastructure is also laid for more general investigations in the future

Almost Commuting Elements in Compact Lie Groups

Armand Borel,Robert Friedman,John W. Morgan
Almost Commuting Elements in Compact Lie Groups Book PDF

Author : Armand Borel,Robert Friedman,John W. Morgan
Publisher : American Mathematical Soc.
Page : 153 pages
File Size : 43,9 Mb
Release : 2002
Category : Compact groups
ISBN : 9780821827925

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Almost Commuting Elements in Compact Lie Groups by Armand Borel,Robert Friedman,John W. Morgan Pdf

This text describes the components of the moduli space of conjugacy classes of commuting pairs and triples of elements in a compact Lie group. This description is in the extended Dynkin diagram of the simply connected cover, together with the co-root integers and the action of the fundamental group. In the case of three commuting elements, we compute Chern-Simons invariants associated to the corresponding flat bundles over the three-torus, and verify a conjecture of Witten which reveals a surprising symmetry involving the Chern-Simons invariants and the dimensions of the components of the moduli space.

Some Generalized Kac-Moody Algebras with Known Root Multiplicities

Peter Niemann
Some Generalized Kac Moody Algebras with Known Root Multiplicities Book PDF

Author : Peter Niemann
Publisher : American Mathematical Soc.
Page : 119 pages
File Size : 48,5 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821828885

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Some Generalized Kac-Moody Algebras with Known Root Multiplicities by Peter Niemann Pdf

Starting from Borcherds' fake monster Lie algebra, this text construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose space into convex holes, of finite and affine type, similar to the situation in the case of the Leech lattice. As a corollary, we obtain strong upper bounds for the root multiplicities of a number of hyperbolic Lie algebras, including $AE_3$.

Derived $\ell $-Adic Categories for Algebraic Stacks

Kai Behrend
Derived ell Adic Categories for Algebraic Stacks Book PDF

Author : Kai Behrend
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 52,9 Mb
Release : 2003
Category : Algebra, Homological
ISBN : 9780821829295

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Derived $\ell $-Adic Categories for Algebraic Stacks by Kai Behrend Pdf

This text is intended for graduate students and research mathematicians interested in algebraic geometry, category theory and homological algebra.

The Moduli Space of $N=1$ Superspheres with Tubes and the Sewing Operation

Katrina Barron
The Moduli Space of N 1 Superspheres with Tubes and the Sewing Operation Book PDF

Author : Katrina Barron
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 54,7 Mb
Release : 2003
Category : Infinite dimensional Lie algebras
ISBN : 9780821832608

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The Moduli Space of $N=1$ Superspheres with Tubes and the Sewing Operation by Katrina Barron Pdf

Within the framework of complex supergeometry and motivated by two-dimensional genus-zero holomorphic $N = 1$ superconformal field theory, this book defines the moduli space of $N=1$ genus-zero super-Riemann surfaces with oriented and ordered half-infinite tubes, modulo superconformal equivalence.

Mutual Invadability Implies Coexistence in Spatial Models

Richard Durrett
Mutual Invadability Implies Coexistence in Spatial Models Book PDF

Author : Richard Durrett
Publisher : American Mathematical Soc.
Page : 133 pages
File Size : 44,7 Mb
Release : 2002
Category : Biology
ISBN : 9780821827680

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Mutual Invadability Implies Coexistence in Spatial Models by Richard Durrett Pdf

In (1994) Durrett and Levin proposed that the equilibrium behavior of stochastic spatial models could be determined from properties of the solution of the mean field ordinary differential equation (ODE) that is obtained by pretending that all sites are always independent. Here we prove a general result in support of that picture. We give a condition on an ordinary differential equation which implies that densities stay bounded away from 0 in the associated reaction-diffusion equation, and that coexistence occurs in the stochastic spatial model with fast stirring. Then using biologists' notion of invadability as a guide, we show how this condition can be checked in a wide variety of examples that involve two or three species: epidemics, diploid genetics models, predator-prey systems, and various competition models.