Diffusions and Elliptic Operators

2006-05-11 Mathematics

Author : Richard F. Bass
Release : 2006-05-11
Genre : Mathematics
Kind : eBook
Book Rating : 044/5 ( reviews)

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Book Synopsis Diffusions and Elliptic Operators by : Richard F. Bass

Download or read book Diffusions and Elliptic Operators written by Richard F. Bass. This book was released on 2006-05-11. Available in PDF, EPUB and Kindle. Book excerpt: A discussion of the interplay of diffusion processes and partial differential equations with an emphasis on probabilistic methods. It begins with stochastic differential equations, the probabilistic machinery needed to study PDE, and moves on to probabilistic representations of solutions for PDE, regularity of solutions and one dimensional diffusions. The author discusses in depth two main types of second order linear differential operators: non-divergence operators and divergence operators, including topics such as the Harnack inequality of Krylov-Safonov for non-divergence operators and heat kernel estimates for divergence form operators, as well as Martingale problems and the Malliavin calculus. While serving as a textbook for a graduate course on diffusion theory with applications to PDE, this will also be a valuable reference to researchers in probability who are interested in PDE, as well as for analysts interested in probabilistic methods.

Elliptic Partial Differential Equations

2011-03-03 Mathematics

Author : Vitaly Volpert
Release : 2011-03-03
Genre : Mathematics
Kind : eBook
Book Rating : 374/5 ( reviews)

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Book Synopsis Elliptic Partial Differential Equations by : Vitaly Volpert

Download or read book Elliptic Partial Differential Equations written by Vitaly Volpert. This book was released on 2011-03-03. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic partial differential equations has undergone an important development over the last two centuries. Together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications, it has become one of the most richly enhanced fields of mathematics. This monograph undertakes a systematic presentation of the theory of general elliptic operators. The author discusses a priori estimates, normal solvability, the Fredholm property, the index of an elliptic operator, operators with a parameter, and nonlinear Fredholm operators. Particular attention is paid to elliptic problems in unbounded domains which have not yet been sufficiently treated in the literature and which require some special approaches. The book also contains an analysis of non-Fredholm operators and discrete operators as well as extensive historical and bibliographical comments . The selected topics and the author's level of discourse will make this book a most useful resource for researchers and graduate students working in the broad field of partial differential equations and applications.

Heat Kernels for Elliptic and Sub-elliptic Operators

2010-10-10 Mathematics

Author : Ovidiu Calin
Release : 2010-10-10
Genre : Mathematics
Kind : eBook
Book Rating : 956/5 ( reviews)

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Book Synopsis Heat Kernels for Elliptic and Sub-elliptic Operators by : Ovidiu Calin

Download or read book Heat Kernels for Elliptic and Sub-elliptic Operators written by Ovidiu Calin. This book was released on 2010-10-10. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a unified presentation of several theories of finding explicit formulas for heat kernels for both elliptic and sub-elliptic operators. These kernels are important in the theory of parabolic operators because they describe the distribution of heat on a given manifold as well as evolution phenomena and diffusion processes. Heat Kernels for Elliptic and Sub-elliptic Operators is an ideal reference for graduate students, researchers in pure and applied mathematics, and theoretical physicists interested in understanding different ways of approaching evolution operators.

Elliptic Partial Differential Equations

2011-03-06 Mathematics

Author : Vitaly Volpert
Release : 2011-03-06
Genre : Mathematics
Kind : eBook
Book Rating : 366/5 ( reviews)

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Book Synopsis Elliptic Partial Differential Equations by : Vitaly Volpert

Download or read book Elliptic Partial Differential Equations written by Vitaly Volpert. This book was released on 2011-03-06. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic partial differential equations has undergone an important development over the last two centuries. Together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications, it has become one of the most richly enhanced fields of mathematics. This monograph undertakes a systematic presentation of the theory of general elliptic operators. The author discusses a priori estimates, normal solvability, the Fredholm property, the index of an elliptic operator, operators with a parameter, and nonlinear Fredholm operators. Particular attention is paid to elliptic problems in unbounded domains which have not yet been sufficiently treated in the literature and which require some special approaches. The book also contains an analysis of non-Fredholm operators and discrete operators as well as extensive historical and bibliographical comments . The selected topics and the author's level of discourse will make this book a most useful resource for researchers and graduate students working in the broad field of partial differential equations and applications.

Elliptic Operators, Topology, and Asymptotic Methods

2013-12-19 Mathematics

Author : John Roe
Release : 2013-12-19
Genre : Mathematics
Kind : eBook
Book Rating : 836/5 ( reviews)

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Book Synopsis Elliptic Operators, Topology, and Asymptotic Methods by : John Roe

Download or read book Elliptic Operators, Topology, and Asymptotic Methods written by John Roe. This book was released on 2013-12-19. Available in PDF, EPUB and Kindle. Book excerpt: Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important exampl

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Diffusions and Elliptic Operators

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