Foundations Of The Classical Theory Of Partial Differential Equations

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From the reviews: "...I think the volume is a great success ... a welcome addition to the literature ..." The Mathematical Intelligencer, 1993 "... It is comparable in scope with the great Courant-Hilbert Methods of Mathematical Physics, but it is much shorter, more up to date of course, and contains more elaborate analytical machinery...." The Mathematical Gazette, 1993

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Genre : Mathematics
Author : Yu.V. Egorov
Publisher : Springer Science & Business Media
Release : 2013-12-01
File : 264 Pages
ISBN-13 : 9783642580932


Introduction To Second Order Partial Differential Equations An Classical And Variational Solutions

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The book extensively introduces classical and variational partial differential equations (PDEs) to graduate and post-graduate students in Mathematics. The topics, even the most delicate, are presented in a detailed way. The book consists of two parts which focus on second order linear PDEs. Part I gives an overview of classical PDEs, that is, equations which admit strong solutions, verifying the equations pointwise. Classical solutions of the Laplace, heat, and wave equations are provided. Part II deals with variational PDEs, where weak (variational) solutions are considered. They are defined by variational formulations of the equations, based on Sobolev spaces. A comprehensive and detailed presentation of these spaces is given. Examples of variational elliptic, parabolic, and hyperbolic problems with different boundary conditions are discussed.

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Genre : Mathematics
Author : Doina Cioranescu
Publisher : World Scientific Publishing Company
Release : 2017-11-27
File : 298 Pages
ISBN-13 : 9789813229198


Partial Differential Equations Ix

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This EMS volume gives an overview of the modern theory of elliptic boundary value problems, with contributions focusing on differential elliptic boundary problems and their spectral properties, elliptic pseudodifferential operators, and general differential elliptic boundary value problems in domains with singularities.

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Genre : Mathematics
Author : M.S. Agranovich
Publisher : Springer Science & Business Media
Release : 2013-11-11
File : 287 Pages
ISBN-13 : 9783662067215


Qualitative Analysis Of Nonlinear Elliptic Partial Differential Equations

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This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by elliptic partial differential equations. These equations can be seen as nonlinear versions of the classical Laplace equation, and they appear as mathematical models in different branches of physics, chemistry, biology, genetics, and engineering and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on the calculus of variations and functional analysis. Concentrating on single-valued or multivalued elliptic equations with nonlinearities of various types, the aim of this volume is to obtain sharp existence or nonexistence results, as well as decay rates for general classes of solutions. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including bifurcation, stability, asymptotic analysis, and optimal regularity of solutions. The method of presentation should appeal to readers with different backgrounds in functional analysis and nonlinear partial differential equations. All chapters include detailed heuristic arguments providing thorough motivation of the study developed later on in the text, in relationship with concrete processes arising in applied sciences. A systematic description of the most relevant singular phenomena described in this volume includes existence (or nonexistence) of solutions, unicity or multiplicity properties, bifurcation and asymptotic analysis, and optimal regularity. The book includes an extensive bibliography and a rich index, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of nonlinear phenomena described by elliptic partial differential equations.

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Genre : Differential equations, Elliptic
Author : Vicentiu D. Radulescu
Publisher : Hindawi Publishing Corporation
Release : 2008
File : 205 Pages
ISBN-13 : 9789774540394


Probability Theory Iii

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This volume of the Encyclopaedia is a survey of stochastic calculus, an increasingly important part of probability, authored by well-known experts in the field. The book addresses graduate students and researchers in probability theory and mathematical statistics, as well as physicists and engineers who need to apply stochastic methods.

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Genre : Mathematics
Author : Yurij V. Prokhorov
Publisher : Springer Science & Business Media
Release : 2013-03-14
File : 260 Pages
ISBN-13 : 9783662036402


Probability Theory Iii

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This volume of the Encyclopaedia is a survey of stochastic calculus, an increasingly important part of probability, authored by well-known experts in the field. The book addresses graduate students and researchers in probability theory and mathematical statistics, as well as physicists and engineers who need to apply stochastic methods.

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Genre : Business & Economics
Author : Alʹbert Nikolaevich Shiri︠a︡ev
Publisher : Springer Science & Business Media
Release : 1998
File : 272 Pages
ISBN-13 : 3540546871


Computational Models Volume I

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Computational Models is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. Modern Computational Mathematics arises in a wide variety of fields, including business, economics, engineering, finance, medicine and science. The Theme on Computational Models provides the essential aspects of Computational Mathematics emphasizing Basic Methods for Solving Equations; Numerical Analysis and Methods for Ordinary Differential Equations; Numerical Methods and Algorithms; Computational Methods and Algorithms; Numerical Models and Simulation. These two volumes are aimed at those seeking in-depth of advanced knowledge: University and College students Educators, Professional practitioners, Research personnel and Policy analysts, managers, and decision makers and NGOs.

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Author : Shaidurov Vladimir Viktorovich
Publisher : EOLSS Publications
Release : 2009-04-10
File : 542 Pages
ISBN-13 : 9781848260351


Commutative Harmonic Analysis Ii

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Classical harmonic analysis is an important part of modern physics and mathematics, comparable in its significance with calculus. Created in the 18th and 19th centuries as a distinct mathematical discipline it continued to develop, conquering new unexpected areas and producing impressive applications to a multitude of problems. It is widely understood that the explanation of this miraculous power stems from group theoretic ideas underlying practically everything in harmonic analysis. This book is an unusual combination of the general and abstract group theoretic approach with a wealth of very concrete topics attractive to everybody interested in mathematics. Mathematical literature on harmonic analysis abounds in books of more or less abstract or concrete kind, but the lucky combination as in this volume can hardly be found.

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Genre : Mathematics
Author : Viktor Petrovich Khavin
Publisher : Springer Science & Business Media
Release : 1998
File : 340 Pages
ISBN-13 : 354051998X


Representation Theory And Noncommutative Harmonic Analysis I

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This two-part survey provides a short review of the classical part of representation theory, carefully exposing the structure of the theory without overwhelming readers with details, and deals with representations of Virasoro and Kac-Moody algebra. It presents a wealth of recent results on representations of infinite-dimensional groups.

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Genre : Mathematics
Author : Alexandre Kirillov
Publisher : Springer Science & Business Media
Release : 1994-11-23
File : 248 Pages
ISBN-13 : 3540186980


Functional Analysis I

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The twentieth-century view of the analysis of functions is dominated by the study of classes of functions. This volume of the Encyclopaedia covers the origins, development and applications of linear functional analysis, explaining along the way how one is led naturally to the modern approach.

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Genre : Mathematics
Author : Yu.I. Lyubich
Publisher : Springer Science & Business Media
Release : 2013-03-09
File : 290 Pages
ISBN-13 : 9783662028490