A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials write by Florica C. Cirstea. This book was released on 2014-10-03. A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials available in PDF, EPUB and Kindle. 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
A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials write by Florica C. Cîrstea. This book was released on 2014-01-08. A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials available in PDF, EPUB and Kindle. 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
Isolated Singularities in Partial Differential Inequalities - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Isolated Singularities in Partial Differential Inequalities write by Marius Ghergu. This book was released on 2016-01-25. Isolated Singularities in Partial Differential Inequalities available in PDF, EPUB and Kindle. 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
Generalized Descriptive Set Theory and Classification Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Generalized Descriptive Set Theory and Classification Theory write by Sy-David Friedman. This book was released on 2014-06-05. Generalized Descriptive Set Theory and Classification Theory available in PDF, EPUB and Kindle. 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
Julia Sets and Complex Singularities of Free Energies - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Julia Sets and Complex Singularities of Free Energies write by Jianyong Qiao. This book was released on 2015-02-06. Julia Sets and Complex Singularities of Free Energies available in PDF, EPUB and Kindle. 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.
