Elliptic Partial Differential Equations of Second Order

Author: David Gilbarg,Neil S. Trudinger

Publisher: Springer

ISBN: 3642617980

Category: Mathematics

Page: 518

View: 361

From the reviews: "This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student." --New Zealand Mathematical Society, 1985
Posted in Mathematics

Stable Solutions of Elliptic Partial Differential Equations

Author: Louis Dupaigne

Publisher: CRC Press

ISBN: 1420066552

Category: Mathematics

Page: 335

View: 8824

Stable solutions are ubiquitous in differential equations. They represent meaningful solutions from a physical point of view and appear in many applications, including mathematical physics (combustion, phase transition theory) and geometry (minimal surfaces). Stable Solutions of Elliptic Partial Differential Equations offers a self-contained presentation of the notion of stability in elliptic partial differential equations (PDEs). The central questions of regularity and classification of stable solutions are treated at length. Specialists will find a summary of the most recent developments of the theory, such as nonlocal and higher-order equations. For beginners, the book walks you through the fine versions of the maximum principle, the standard regularity theory for linear elliptic equations, and the fundamental functional inequalities commonly used in this field. The text also includes two additional topics: the inverse-square potential and some background material on submanifolds of Euclidean space.
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Elliptic Partial Differential Equations

Existence and Regularity of Distributional Solutions

Author: Lucio Boccardo,Gisella Croce

Publisher: Walter de Gruyter

ISBN: 3110315424

Category: Mathematics

Page: 201

View: 9186

Elliptic partial differential equations is one of the main and most active areas in mathematics. In our book we study linear and nonlinear elliptic problems in divergence form, with the aim of providing classical results, as well as more recent developments about distributional solutions. For this reason the book is addressed to master's students, PhD students and anyone who wants to begin research in this mathematical field.
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Variational Techniques for Elliptic Partial Differential Equations

Theoretical Tools and Advanced Applications

Author: Francisco J. Sayas,Thomas S. Brown,Matthew E. Hassell

Publisher: CRC Press

ISBN: 0429016190

Category: Mathematics

Page: 512

View: 6706

Variational Techniques for Elliptic Partial Differential Equations, intended for graduate students studying applied math, analysis, and/or numerical analysis, provides the necessary tools to understand the structure and solvability of elliptic partial differential equations. Beginning with the necessary definitions and theorems from distribution theory, the book gradually builds the functional analytic framework for studying elliptic PDE using variational formulations. Rather than introducing all of the prerequisites in the first chapters, it is the introduction of new problems which motivates the development of the associated analytical tools. In this way the student who is encountering this material for the first time will be aware of exactly what theory is needed, and for which problems. Features A detailed and rigorous development of the theory of Sobolev spaces on Lipschitz domains, including the trace operator and the normal component of vector fields An integration of functional analysis concepts involving Hilbert spaces and the problems which can be solved with these concepts, rather than separating the two Introduction to the analytical tools needed for physical problems of interest like time-harmonic waves, Stokes and Darcy flow, surface differential equations, Maxwell cavity problems, etc. A variety of problems which serve to reinforce and expand upon the material in each chapter, including applications in fluid and solid mechanics
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Handbook of geometric analysis

Author: Lizhen Ji

Publisher: Intl Pr of Boston Inc

ISBN: 9781571461308

Category: Mathematics

Page: 676

View: 806

Geometric Analysis combines differential equations with differential geometry. An important aspect of geometric analysis is to approach geometric problems by studying differential equations. Besides some known linear differential operators such as the Laplace operator, many differential equations arising from differential geometry are nonlinear. A particularly important example is the Monge-Amperè equation. Applications to geometric problems have also motivated new methods and techniques in differential equations. The field of geometric analysis is broad and has had many striking applications.This handbook of geometric analysis—the first of the two to be published in the ALM series—presents introductions and survey papers treating important topics in geometric analysis, with their applications to related fields. It can be used as a reference by graduate students and by researchers in related areas.
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DCDS-A

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 9592

Posted in Mathematics

BIT.

Numerical mathematics

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Computers

Page: N.A

View: 967

Posted in Computers

Methoden der Mathematischen Physik

Author: Richard Courant,David Hilbert

Publisher: Springer-Verlag

ISBN: 366236445X

Category: Mathematics

Page: 454

View: 3563

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
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Nichtlineare Funktionalanalysis

Eine Einführung

Author: Michael Ruzicka

Publisher: Springer-Verlag

ISBN: 3540350225

Category: Mathematics

Page: 208

View: 1590

Das vorliegende Lehrbuch enthält eine Einführung in die nichtlineare Funktionalanalysis. Die Themenauswahl beinhaltet Methoden und Techniken, die, neben dem allgemeinen Interesse, bei der Untersuchung von nichtlinearen elliptischen und parabolischen partiellen Differentialgleichungen benutzt werden. Es wird insbesondere auf Fixpunktsätze, Differentiation und Integration in Banachräumen, monotone Operatoren und den Abbildungsgrad eingegangen. Der Darstellung des Stoffes liegt das Zusammenspiel und die gegenseitige Beeinflussung von Theorie und Anwendungen zugrunde. Kurze Einführungen am Kapitelanfang, illustrative Beispiele sowie die detaillierte Herleitung von Ergebnissen erleichtern das Verständnis. Ein Appendix mit einer Kurzzusammenfassung von Ergebnissen aus der linearen Funktionalanalysis rundet die Darstellung ab. Das Buch richtet sich an Studierende ab dem 6. Semester und umfasst den Lehrstoff für ein Semester.
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Proceedings of the St. Petersburg Mathematical Society, Volume XV

Advances in Mathematical Analysis of Partial Differential Equations

Author: Darya Apushkinskaya,Alexander I. Nazarov

Publisher: American Mathematical Society

ISBN: 1470415518

Category: Mathematics

Page: 270

View: 1240

This book presents the proceedings of the international workshop, "Advances in Mathematical Analysis of Partial Differential Equations" held at the Institut Mittag-Leffler, Stockholm, Sweden, July 9-13, 2012, dedicated to the memory of the outstanding Russian mathematician Olga A. Ladyzhenskaya. The volume contains papers that engage a wide set of modern topics in the theory of linear and nonlinear partial differential equations and applications, including variational and free boundary problems, mathematical problems of hydrodynamics, and magneto-geostrophic equations.
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A Course in Mathematical Analysis Volume 3

Variation of Solutions; Partial Differential Equations of the Second Order; Integral Equations; Calculus of Variations

Author: Edouard Goursat,Howard G. Bergmann

Publisher: Courier Corporation

ISBN: 0486446522

Category: Mathematics

Page: 752

View: 3995

Classic three-volume study. Volume 1 covers applications to geometry, expansion in series, definite integrals, and derivatives and differentials. Volume 2 explores functions of a complex variable and differential equations. Volume 3 surveys variations of solutions and partial differential equations of the second order and integral equations and calculus of variations.
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Topologie

Author: Klaus Jänich

Publisher: Springer-Verlag

ISBN: 3662105756

Category: Mathematics

Page: 241

View: 359

Aus den Rezensionen: "Was das Buch vor allem auszeichnet, ist die unkonventionelle Darstellungsweise. Hier wird Mathematik nicht im trockenen Definition-Satz-Beweis-Stil geboten, sondern sie wird dem Leser pointiert und mit viel Humor schmackhaft gemacht. In ungewöhnlich fesselnder Sprache geschrieben, ist die Lektüre dieses Buches auch ein belletristisches Vergnügen. Fast 200 sehr instruktive und schöne Zeichnungen unterstützen das Verständnis, motivieren die behandelten Aussagen, modellieren die tragenden Beweisideen heraus. Ungewöhnlich ist auch das Register, das unter jedem Stichwort eine Kurzdefinition enthält und somit umständliches Nachschlagen erspart". Wiss. Zeitschrift der TU Dresden Jetzt in der siebenten, durchgesehenen Auflage!
Posted in Mathematics