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Local And Global Aspects Of Quasilinear Degenerate Elliptic Equations Quasilinear Elliptic Singular Problems
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Book Synopsis Local And Global Aspects Of Quasilinear Degenerate Elliptic Equations: Quasilinear Elliptic Singular Problems by : Laurent Veron
Download or read book Local And Global Aspects Of Quasilinear Degenerate Elliptic Equations: Quasilinear Elliptic Singular Problems written by Laurent Veron and published by World Scientific. This book was released on 2017-05-05 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of elliptic second-order degenerate quasilinear equations, the model of which is the p-Laplacian, with or without dominant lower order reaction term. Emphasis is put on three aspects:
Book Synopsis Local and Global Aspects of Quasilinear Degenerate Elliptic Equations by : Laurent Veron
Download or read book Local and Global Aspects of Quasilinear Degenerate Elliptic Equations written by Laurent Veron and published by World Scientific Publishing Company. This book was released on 2016-09-30 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of elliptic second-order degenerate quasilinear equations, the model of which is the p-Laplacian, with or without dominant lower order reaction term. Emphasis is put on three aspects: The existence of separable singular solutions enables the description of isolated singularities of general solutions. The construction of singular solutions is delicate and cannot be done without the understanding of the spherical p-harmonic eigenvalue problem. When the equations are considered on a Riemannian manifold, existence or non-existence of solutions depends on geometric assumptions such as the curvature. A priori estimates and Liouville type problems are analyzed. When the equations are considered with a forcing term in the class of measures, their study is strongly linked to the properties of a class of potentials appearing in harmonic analysis such as the Riesz, the Bessel or the Wolff potentials and to their associated capacities. Necessary and sufficient conditions for existence of solutions link the continuity of the measure with respect to some appropriate capacity.
Book Synopsis Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs by : Emanuel Indrei
Download or read book Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs written by Emanuel Indrei and published by American Mathematical Society. This book was released on 2023-01-09 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the virtual conference on Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs, held from February 28–March 1, 2021, and hosted by Purdue University, West Lafayette, IN. The mathematical content of this volume is at the intersection of viscosity theory, Fourier analysis, mass transport theory, fractional elliptic theory, and geometric analysis. The reader will encounter, among others, the following topics: the principal-agent problem; Maxwell's equations; Liouville-type theorems for fully nonlinear elliptic equations; a doubly monotone flow for constant width bodies; and the edge dislocations problem for crystals that describes the equilibrium configurations by a nonlocal fractional Laplacian equation.
Book Synopsis Nonlinear Elliptic Partial Differential Equations by : J. P. Gossez
Download or read book Nonlinear Elliptic Partial Differential Equations written by J. P. Gossez and published by American Mathematical Soc.. This book was released on 2011 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers on semi-linear and quasi-linear elliptic equations from the workshop on Nonlinear Elliptic Partial Differential Equations, in honor of Jean-Pierre Gossez's 65th birthday, held September 2-4, 2009 at the Universite Libre de Bruxelles, Belgium. The workshop reflected Gossez's contributions in nonlinear elliptic PDEs and provided an opening to new directions in this very active research area. Presentations covered recent progress in Gossez's favorite topics, namely various problems related to the $p$-Laplacian operator, the antimaximum principle, the Fucik Spectrum, and other related subjects. This volume will be of principle interest to researchers in nonlinear analysis, especially in partial differential equations of elliptic type.
Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States II by : W.-M. Ni
Download or read book Nonlinear Diffusion Equations and Their Equilibrium States II written by W.-M. Ni and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = ~U + f(u). Here ~ denotes the n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time domain of the form n x [O,T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its time-independent counterpart, the elliptic equation of equilibrium ~u+f(u)=O. Particular cases arise, for example, in population genetics, the physics of nu clear stability, phase transitions between liquids and gases, flows in porous media, the Lend-Emden equation of astrophysics, various simplified com bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc ture of the nonlinear function f(u) influences the behavior of the solution.
Book Synopsis Stability Theory of Differential Equations by : Richard Bellman
Download or read book Stability Theory of Differential Equations written by Richard Bellman and published by Courier Corporation. This book was released on 2013-02-20 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies. The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from the beginning. In regard to the stability of nonlinear systems, results of the linear theory are used to drive the results of Poincaré and Liapounoff. Professor Bellman then surveys important results concerning the boundedness, stability, and asymptotic behavior of second-order linear differential equations. The final chapters explore significant nonlinear differential equations whose solutions may be completely described in terms of asymptotic behavior. Only real solutions of real equations are considered, and the treatment emphasizes the behavior of these solutions as the independent variable increases without limit.
Book Synopsis Proceedings of the Conference on Differential & Difference Equations and Applications by : Ravi P. Agarwal
Download or read book Proceedings of the Conference on Differential & Difference Equations and Applications written by Ravi P. Agarwal and published by Hindawi Publishing Corporation. This book was released on 2006 with total page 1266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Singularities of Solutions of Second-Order Quasilinear Equations by : Laurent Veron
Download or read book Singularities of Solutions of Second-Order Quasilinear Equations written by Laurent Veron and published by CRC Press. This book was released on 1996-08-01 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text examines the singularity problem for solutions of elliptic and parabolic quasilinear equations of second order.
Book Synopsis Function Spaces, Differential Operators and Nonlinear Analysis by : Dorothee Haroske
Download or read book Function Spaces, Differential Operators and Nonlinear Analysis written by Dorothee Haroske and published by Birkhäuser. This book was released on 2012-12-06 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to our teacher and friend Hans Triebel. The core of the book is based on lectures given at the International Conference "Function Spaces, Differential Operators and Nonlinear Analysis" (FSDONA--01) held in Teistungen, Thuringia / Germany, from June 28 to July 4,2001, in honour of his 65th birthday. This was the fifth in a series of meetings organised under the same name by scientists from Finland (Helsinki, Oulu) , the Czech Republic (Prague, Plzen) and Germany (Jena) promoting the collaboration of specialists in East and West, working in these fields. This conference was a very special event because it celebrated Hans Triebel's extraordinary impact on mathematical analysis. The development of the mod ern theory of function spaces in the last 30 years and its application to various branches in both pure and applied mathematics is deeply influenced by his lasting contributions. In a series of books Hans Triebel has given systematic treatments of the theory of function spaces from different points of view, thus revealing its interdependence with interpolation theory, harmonic analysis, partial differential equations, nonlinear operators, entropy, spectral theory and, most recently, anal ysis on fractals. The presented collection of papers is a tribute to Hans Triebel's distinguished work. The book is subdivided into three parts: • Part I contains the two invited lectures by O.V. Besov (Moscow) and D.E. Edmunds (Sussex) having a survey character and honouring Hans Triebel's contributions.
Book Synopsis Fully Nonlinear Elliptic Equations by : Luis A. Caffarelli
Download or read book Fully Nonlinear Elliptic Equations written by Luis A. Caffarelli and published by American Mathematical Soc.. This book was released on 1995 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equations, the Alexandroff estimate and Krylov-Safonov Harnack-type inequality for viscosity solutions, uniqueness theory for viscosity solutions, Evans and Krylov regularity theory for convex fully nonlinear equations, and regularity theory for fully nonlinear equations with variable coefficients.
Book Synopsis Handbook of Differential Equations: Stationary Partial Differential Equations by : Michel Chipot
Download or read book Handbook of Differential Equations: Stationary Partial Differential Equations written by Michel Chipot and published by Elsevier. This book was released on 2007-05-03 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of self contained state-of-the art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching.- written by well-known experts in the field- self contained volume in series covering one of the most rapid developing topics in mathematics
Book Synopsis Harmonic Analysis and Partial Differential Equations by : Anatoly Golberg
Download or read book Harmonic Analysis and Partial Differential Equations written by Anatoly Golberg and published by Springer Nature. This book was released on 2023-04-26 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Vladimir Maz'ya has made a number of groundbreaking contributions to numerous areas of mathematics, including partial differential equations, function theory, and harmonic analysis. The chapters in this volume - compiled on the occasion of his 80th birthday - are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.
Book Synopsis Evolution Equations by : Gisele Ruiz Goldstein
Download or read book Evolution Equations written by Gisele Ruiz Goldstein and published by CRC Press. This book was released on 2003-06-24 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celebrating the work of renowned mathematician Jerome A. Goldstein, this reference compiles original research on the theory and application of evolution equations to stochastics, physics, engineering, biology, and finance. The text explores a wide range of topics in linear and nonlinear semigroup theory, operator theory, functional analysis, and linear and nonlinear partial differential equations, and studies the latest theoretical developments and uses of evolution equations in a variety of disciplines. Providing nearly 500 references, the book contains discussions by renowned mathematicians such as H. Brezis, G. Da Prato, N.E. Gretskij, I. Lasiecka, Peter Lax, M. M. Rao, and R. Triggiani.
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1770 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 and published by American Mathematical Soc.. This book was released on 2014-01-08 with total page 97 pages. 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.
Book Synopsis Nonlinear Partial Differential Equations and Related Topics by : Arina A. Arkhipova
Download or read book Nonlinear Partial Differential Equations and Related Topics written by Arina A. Arkhipova and published by American Mathematical Soc.. This book was released on 2010 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: "St. Petersburg PDE seminar, special session dedicated to N.N. Uraltseva's [75th] anniversary, June 2009"--P. [vi].
Book Synopsis Partial Differential Inequalities with Nonlinear Convolution Terms by : Marius Ghergu
Download or read book Partial Differential Inequalities with Nonlinear Convolution Terms written by Marius Ghergu and published by Springer Nature. This book was released on 2023-01-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief research monograph uses modern mathematical methods to investigate partial differential equations with nonlinear convolution terms, enabling readers to understand the concept of a solution and its asymptotic behavior. In their full generality, these inequalities display a non-local structure. Classical methods, such as maximum principle or sub- and super-solution methods, do not apply to this context. This work discusses partial differential inequalities (instead of differential equations) for which there is no variational setting. This current work brings forward other methods that prove to be useful in understanding the concept of a solution and its asymptotic behavior related to partial differential inequalities with nonlinear convolution terms. It promotes and illustrates the use of a priori estimates, Harnack inequalities, and integral representation of solutions. One of the first monographs on this rapidly expanding field, the present work appeals to graduate and postgraduate students as well as to researchers in the field of partial differential equations and nonlinear analysis.
