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A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials

2014-10-03 Differential equations, Elliptic
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Release : 2014-10-03
Genre : Differential equations, Elliptic
Kind : eBook
Book Rating : 290/5 ( reviews)

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Book Synopsis A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials by : Florica C. Cirstea

Download or read book A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials written by Florica C. Cirstea. This book was released on 2014-10-03. Available in PDF, EPUB and Kindle. Book excerpt: Volume 227, number 1068 (fourth of 4 numbers), January 2014.

A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials

2014-01-08 Mathematics
Download A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials PDF Online Free

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Release : 2014-01-08
Genre : Mathematics
Kind : eBook
Book Rating : 220/5 ( reviews)

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Book Synopsis A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials by : Florica C. Cîrstea

Download or read book A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials written by Florica C. Cîrstea. This book was released on 2014-01-08. Available in PDF, EPUB and Kindle. Book excerpt: In particular, for b = 1 and λ = 0, we find a sharp condition on h such that the origin is a removable singularity for all non-negative solutions of [[eqref]]one, thus addressing an open question of Vázquez and Véron.

Isolated Singularities in Partial Differential Inequalities

2016-01-25 Mathematics
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Release : 2016-01-25
Genre : Mathematics
Kind : eBook
Book Rating : 574/5 ( reviews)

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Book Synopsis Isolated Singularities in Partial Differential Inequalities by : Marius Ghergu

Download or read book Isolated Singularities in Partial Differential Inequalities written by Marius Ghergu. This book was released on 2016-01-25. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, the authors present some powerful methods for dealing with singularities in elliptic and parabolic partial differential inequalities. Here, the authors take the unique approach of investigating differential inequalities rather than equations, the reason being that the simplest way to study an equation is often to study a corresponding inequality; for example, using sub and superharmonic functions to study harmonic functions. Another unusual feature of the present book is that it is based on integral representation formulae and nonlinear potentials, which have not been widely investigated so far. This approach can also be used to tackle higher order differential equations. The book will appeal to graduate students interested in analysis, researchers in pure and applied mathematics, and engineers who work with partial differential equations. Readers will require only a basic knowledge of functional analysis, measure theory and Sobolev spaces.

Generalized Descriptive Set Theory and Classification Theory

2014-06-05 Mathematics
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Release : 2014-06-05
Genre : Mathematics
Kind : eBook
Book Rating : 757/5 ( reviews)

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Book Synopsis Generalized Descriptive Set Theory and Classification Theory by : Sy-David Friedman

Download or read book Generalized Descriptive Set Theory and Classification Theory written by Sy-David Friedman. This book was released on 2014-06-05. Available in PDF, EPUB and Kindle. Book excerpt: Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper the authors study the generalization where countable is replaced by uncountable. They explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. They also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. The authors' results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.

Julia Sets and Complex Singularities of Free Energies

2015-02-06 Mathematics
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Release : 2015-02-06
Genre : Mathematics
Kind : eBook
Book Rating : 828/5 ( reviews)

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Book Synopsis Julia Sets and Complex Singularities of Free Energies by : Jianyong Qiao

Download or read book Julia Sets and Complex Singularities of Free Energies written by Jianyong Qiao. This book was released on 2015-02-06. Available in PDF, EPUB and Kindle. Book excerpt: The author studies a family of renormalization transformations of generalized diamond hierarchical Potts models through complex dynamical systems. He proves that the Julia set (unstable set) of a renormalization transformation, when it is treated as a complex dynamical system, is the set of complex singularities of the free energy in statistical mechanics. He gives a sufficient and necessary condition for the Julia sets to be disconnected. Furthermore, he proves that all Fatou components (components of the stable sets) of this family of renormalization transformations are Jordan domains with at most one exception which is completely invariant. In view of the problem in physics about the distribution of these complex singularities, the author proves here a new type of distribution: the set of these complex singularities in the real temperature domain could contain an interval. Finally, the author studies the boundary behavior of the first derivative and second derivative of the free energy on the Fatou component containing the infinity. He also gives an explicit value of the second order critical exponent of the free energy for almost every boundary point.

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