Non-Divergence Equations Structured on Hormander Vector Fields: Heat Kernels and Harnack Inequalities

Non-Divergence Equations Structured on Hormander Vector Fields: Heat Kernels and Harnack Inequalities
Title Non-Divergence Equations Structured on Hormander Vector Fields: Heat Kernels and Harnack Inequalities PDF eBook
Author Marco Bramanti
Publisher American Mathematical Soc.
Pages 136
Release 2010
Genre Mathematics
ISBN 0821849034

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"March 2010, Volume 204, number 961 (end of volume)."

An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields

An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields
Title An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields PDF eBook
Author Marco Bramanti
Publisher Springer Science & Business Media
Pages 157
Release 2013-11-20
Genre Mathematics
ISBN 3319020870

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​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.

Geometric Analysis and PDEs

Geometric Analysis and PDEs
Title Geometric Analysis and PDEs PDF eBook
Author Matthew J. Gursky
Publisher Springer
Pages 296
Release 2009-07-31
Genre Mathematics
ISBN 364201674X

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This volume contains lecture notes on key topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics.

Geometric Methods in PDE’s

Geometric Methods in PDE’s
Title Geometric Methods in PDE’s PDF eBook
Author Giovanna Citti
Publisher Springer
Pages 381
Release 2015-10-31
Genre Mathematics
ISBN 3319026666

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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.

$C^*$-Algebras of Homoclinic and Heteroclinic Structure in Expansive Dynamics

$C^*$-Algebras of Homoclinic and Heteroclinic Structure in Expansive Dynamics
Title $C^*$-Algebras of Homoclinic and Heteroclinic Structure in Expansive Dynamics PDF eBook
Author Klaus Thomsen
Publisher American Mathematical Soc.
Pages 138
Release 2010-06-11
Genre Mathematics
ISBN 0821846922

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The author unifies various constructions of $C^*$-algebras from dynamical systems, specifically, the dimension group construction of Krieger for shift spaces, the corresponding constructions of Wagoner and Boyle, Fiebig and Fiebig for countable state Markov shifts and one-sided shift spaces, respectively, and the constructions of Ruelle and Putnam for Smale spaces. The general setup is used to analyze the structure of the $C^*$-algebras arising from the homoclinic and heteroclinic equivalence relations in expansive dynamical systems, in particular, expansive group endomorphisms and automorphisms and generalized 1-solenoids. For these dynamical systems it is shown that the $C^*$-algebras are inductive limits of homogeneous or sub-homogeneous algebras with one-dimensional spectra.

Resistance Forms, Quasisymmetric Maps and Heat Kernel Estimates

Resistance Forms, Quasisymmetric Maps and Heat Kernel Estimates
Title Resistance Forms, Quasisymmetric Maps and Heat Kernel Estimates PDF eBook
Author Jun Kigami
Publisher American Mathematical Soc.
Pages 145
Release 2012-02-22
Genre Mathematics
ISBN 082185299X

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Assume that there is some analytic structure, a differential equation or a stochastic process for example, on a metric space. To describe asymptotic behaviors of analytic objects, the original metric of the space may not be the best one. Every now and then one can construct a better metric which is somehow ``intrinsic'' with respect to the analytic structure and under which asymptotic behaviors of the analytic objects have nice expressions. The problem is when and how one can find such a metric. In this paper, the author considers the above problem in the case of stochastic processes associated with Dirichlet forms derived from resistance forms. The author's main concerns are the following two problems: (I) When and how to find a metric which is suitable for describing asymptotic behaviors of the heat kernels associated with such processes. (II) What kind of requirement for jumps of a process is necessary to ensure good asymptotic behaviors of the heat kernels associated with such processes.

Maximal Subellipticity

Maximal Subellipticity
Title Maximal Subellipticity PDF eBook
Author Brian Street
Publisher Walter de Gruyter GmbH & Co KG
Pages 768
Release 2023-07-03
Genre Mathematics
ISBN 3111085643

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Maximally subelliptic partial differential equations (PDEs) are a far-reaching generalization of elliptic PDEs. Elliptic PDEs hold a special place: sharp results are known for general linear and even fully nonlinear elliptic PDEs. Over the past half-century, important results for elliptic PDEs have been generalized to maximally subelliptic PDEs. This text presents this theory and generalizes the sharp, interior regularity theory for general linear and fully nonlinear elliptic PDEs to the maximally subelliptic setting.