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Author : Serena Dipierro
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (961 download)
Download or read book Fractional Elliptic Problems with Critical Growth in the Whole of Rn written by Serena Dipierro and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Serena Dipierro
Publisher : Springer
ISBN 13 : 8876426019
Total Pages : 155 pages
Book Rating : 4.8/5 (764 download)
Download or read book Fractional Elliptic Problems with Critical Growth in the Whole of $\R^n$ written by Serena Dipierro and published by Springer. This book was released on 2017-03-14 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are devoted to the analysis of a nonlocal equation in the whole of Euclidean space. In studying this equation, all the necessary material is introduced in the most self-contained way possible, giving precise references to the literature when necessary. The results presented are original, but no particular prerequisite or knowledge of the previous literature is needed to read this text. The work is accessible to a wide audience and can also serve as introductory research material on the topic of nonlocal nonlinear equations.
Author : Donatella Danielli
Publisher : American Mathematical Soc.
ISBN 13 : 1470441101
Total Pages : 214 pages
Book Rating : 4.4/5 (74 download)
Download or read book New Developments in the Analysis of Nonlocal Operators written by Donatella Danielli and published by American Mathematical Soc.. This book was released on 2019-02-21 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on New Developments in the Analysis of Nonlocal Operators, held from October 28–30, 2016, at the University of St. Thomas, Minneapolis, Minnesota. Over the last decade there has been a resurgence of interest in problems involving nonlocal operators, motivated by applications in many areas such as analysis, geometry, and stochastic processes. Problems represented in this volume include uniqueness for weak solutions to abstract parabolic equations with fractional time derivatives, the behavior of the one-phase Bernoulli-type free boundary near a fixed boundary and its relation to a Signorini-type problem, connections between fractional powers of the spherical Laplacian and zeta functions from the analytic number theory and differential geometry, and obstacle problems for a class of not stable-like nonlocal operators for asset price models widely used in mathematical finance. The volume also features a comprehensive introduction to various aspects of the fractional Laplacian, with many historical remarks and an extensive list of references, suitable for beginners and more seasoned researchers alike.
Author : Vincenzo Ambrosio
Publisher : Springer Nature
ISBN 13 : 3030602206
Total Pages : 669 pages
Book Rating : 4.0/5 (36 download)
Download or read book Nonlinear Fractional Schrödinger Equations in R^N written by Vincenzo Ambrosio and published by Springer Nature. This book was released on 2021-04-19 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents recent results concerning nonlinear fractional elliptic problems in the whole space. More precisely, it investigates the existence, multiplicity and qualitative properties of solutions for fractional Schrödinger equations by applying suitable variational and topological methods. The book is mainly intended for researchers in pure and applied mathematics, physics, mechanics, and engineering. However, the material will also be useful for students in higher semesters and young researchers, as well as experienced specialists working in the field of nonlocal PDEs. This is the first book to approach fractional nonlinear Schrödinger equations by applying variational and topological methods.
Author : Giovanni Molica Bisci
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110648938
Total Pages : 191 pages
Book Rating : 4.1/5 (16 download)
Download or read book Nonlinear Problems with Lack of Compactness written by Giovanni Molica Bisci and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-02-08 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative book presents recent research results on nonlinear problems with lack of compactness. The topics covered include several nonlinear problems in the Euclidean setting as well as variational problems on manifolds. The combination of deep techniques in nonlinear analysis with applications to a variety of problems make this work an essential source of information for researchers and graduate students working in analysis and PDE's.
Author : Luigi Ambrosio
Publisher : Springer
ISBN 13 : 8876426515
Total Pages : 230 pages
Book Rating : 4.8/5 (764 download)
Download or read book Lectures on Elliptic Partial Differential Equations written by Luigi Ambrosio and published by Springer. This book was released on 2019-01-10 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book originates from the Elliptic PDE course given by the first author at the Scuola Normale Superiore in recent years. It covers the most classical aspects of the theory of Elliptic Partial Differential Equations and Calculus of Variations, including also more recent developments on partial regularity for systems and the theory of viscosity solutions.
Author : Franco Strocchi
Publisher : Springer
ISBN 13 : 8876426604
Total Pages : 115 pages
Book Rating : 4.8/5 (764 download)
Download or read book Symmetry Breaking in the Standard Model written by Franco Strocchi and published by Springer. This book was released on 2019-07-03 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a non-perturbative approach to the symmetry breaking in the standard model, in this way avoiding the critical issues which affect the standard presentations. The debated empirical meaning of global and local gauge symmetries is clarified. The absence of Goldstone bosons in the Higgs mechanism is non-perturbatively explained by the validity of Gauss laws obeyed by the currents which generate the relatedglobal gauge symmetry. The solution of the U(1) problem and the vacuum structure in quantum chromodynamics (QCD) are obtained without recourse to the problematic semiclassical instanton approximation, by rather exploiting the topology of the gauge group.
Author : Alessandro Cellerino
Publisher : Springer
ISBN 13 : 8876426426
Total Pages : 188 pages
Book Rating : 4.8/5 (764 download)
Download or read book Transcriptome Analysis written by Alessandro Cellerino and published by Springer. This book was released on 2018-06-14 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to be an accessible guide for undergraduate and graduate students to the new field of data-driven biology. Next-generation sequencing technologies have put genome-scale analysis of gene expression into the standard toolbox of experimental biologists. Yet, biological interpretation of high-dimensional data is made difficult by the lack of a common language between experimental and data scientists. By combining theory with practical examples of how specific tools were used to obtain novel insights in biology, particularly in the neurosciences, the book intends to teach students how to design, analyse, and extract biological knowledge from transcriptome sequencing experiments. Undergraduate and graduate students in biomedical and quantitative sciences will benefit from this text as well as academics untrained in the subject.
Author : Alessandra Lunardi
Publisher : Springer
ISBN 13 : 8876426388
Total Pages : 199 pages
Book Rating : 4.8/5 (764 download)
Download or read book Interpolation Theory written by Alessandra Lunardi and published by Springer. This book was released on 2018-05-05 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the third edition of the 1999 lecture notes of the courses on interpolation theory that the author delivered at the Scuola Normale in 1998 and 1999. In the mathematical literature there are many good books on the subject, but none of them is very elementary, and in many cases the basic principles are hidden below great generality. In this book the principles of interpolation theory are illustrated aiming at simplification rather than at generality. The abstract theory is reduced as far as possible, and many examples and applications are given, especially to operator theory and to regularity in partial differential equations. Moreover the treatment is self-contained, the only prerequisite being the knowledge of basic functional analysis.
Author : Pammy Manchanda
Publisher : Springer Nature
ISBN 13 : 981150928X
Total Pages : 431 pages
Book Rating : 4.8/5 (115 download)
Download or read book Mathematical Modelling, Optimization, Analytic and Numerical Solutions written by Pammy Manchanda and published by Springer Nature. This book was released on 2020-02-04 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses a variety of topics related to industrial and applied mathematics, focusing on wavelet theory, sampling theorems, inverse problems and their applications, partial differential equations as a model of real-world problems, computational linguistics, mathematical models and methods for meteorology, earth systems, environmental and medical science, and the oil industry. It features papers presented at the International Conference in Conjunction with 14th Biennial Conference of ISIAM, held at Guru Nanak Dev University, Amritsar, India, on 2–4 February 2018. The conference has emerged as an influential forum, bringing together prominent academic scientists, experts from industry, and researchers. The topics discussed include Schrodinger operators, quantum kinetic equations and their application, extensions of fractional integral transforms, electrical impedance tomography, diffuse optical tomography, Galerkin method by using wavelets, a Cauchy problem associated with Korteweg–de Vries equation, and entropy solution for scalar conservation laws. This book motivates and inspires young researchers in the fields of industrial and applied mathematics.
Author : Claudia Bucur
Publisher : Springer
ISBN 13 : 3319287397
Total Pages : 155 pages
Book Rating : 4.3/5 (192 download)
Download or read book Nonlocal Diffusion and Applications written by Claudia Bucur and published by Springer. This book was released on 2016-04-08 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: Working in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrödinger equations are given. Furthermore, an example of an s-harmonic function, its harmonic extension and some insight into a fractional version of a classical conjecture due to De Giorgi are presented. Although the aim is primarily to gather some introductory material concerning applications of the fractional Laplacian, some of the proofs and results are new. The work is entirely self-contained, and readers who wish to pursue related subjects of interest are invited to consult the rich bibliography for guidance.
Author : Giovanni Molica Bisci
Publisher : Cambridge University Press
ISBN 13 : 1316571696
Total Pages : 401 pages
Book Rating : 4.3/5 (165 download)
Download or read book Variational Methods for Nonlocal Fractional Problems written by Giovanni Molica Bisci and published by Cambridge University Press. This book was released on 2016-03-11 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, including topology, functional analysis, mathematical physics, and potential theory.
Author : Lucio Boccardo
Publisher : Walter de Gruyter
ISBN 13 : 3110315424
Total Pages : 204 pages
Book Rating : 4.1/5 (13 download)
Download or read book Elliptic Partial Differential Equations written by Lucio Boccardo and published by Walter de Gruyter. This book was released on 2013-10-29 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elliptic partial differential equations is one of the main and most active areas in mathematics. This book is devoted to the study of 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 this monograph is addressed to master's students, PhD students and anyone who wants to begin research in this mathematical field.
Author : Chu-Hui He
Publisher : Frontiers Media SA
ISBN 13 : 2832539637
Total Pages : 132 pages
Book Rating : 4.8/5 (325 download)
Download or read book Analytical Methods for Nonlinear Oscillators and Solitary Waves written by Chu-Hui He and published by Frontiers Media SA. This book was released on 2023-11-24 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most well-known analytical method is the perturbation method, which has led to the great discovery of Neptune in 1846, and since then mathematical prediction and empirical observation became two sides of a coin in physics. However, the perturbation method is based on the small parameter assumption, and the obtained solutions are valid only for weakly nonlinear equations, which have greatly limited their applications to modern physical problems. To overcome the shortcomings, many mathematicians and physicists have been extensively developing various technologies for several centuries, however, there is no universal method for all nonlinear problems, and mathematical prediction with remarkably high accuracy is still much needed for modern physics, for example, the solitary waves traveling along an unsmooth boundary, the low-frequency property of a harvesting energy device, the pull-in voltage in a micro-electromechanical system. Now various effective analytical methods have appeared in the open literature, e.g., the homotopy perturbation method and the variational iteration method. An analytical solution provides a fast insight into its physical properties of a practical problem, e.g., frequency-amplitude relation of a nonlinear oscillator, solitary wave in an optical fiber, pull-in instability of a microelectromechanical system, making mathematical prediction even more attractive in modern physics. Nonlinear physics has been developing into a new stage, where the fractal-fractional differential equations have to be adopted to describe more accurately discontinuous problems, and it becomes ever more difficult to find an analytical solution for such nonlinear problems, and the analytical methods for fractal-fractional differential equations have laid the foundations for nonlinear physics.
Author : Vladimir Maz'ya
Publisher : Springer Science & Business Media
ISBN 13 : 3642155642
Total Pages : 882 pages
Book Rating : 4.6/5 (421 download)
Download or read book Sobolev Spaces written by Vladimir Maz'ya and published by Springer Science & Business Media. This book was released on 2011-02-11 with total page 882 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool in approximation theory, spectral theory, differential geometry etc. The theory of these spaces is of interest in itself being a beautiful domain of mathematics. The present volume includes basics on Sobolev spaces, approximation and extension theorems, embedding and compactness theorems, their relations with isoperimetric and isocapacitary inequalities, capacities with applications to spectral theory of elliptic differential operators as well as pointwise inequalities for derivatives. The selection of topics is mainly influenced by the author’s involvement in their study, a considerable part of the text is a report on his work in the field. Part of this volume first appeared in German as three booklets of Teubner-Texte zur Mathematik (1979, 1980). In the Springer volume “Sobolev Spaces”, published in English in 1985, the material was expanded and revised. The present 2nd edition is enhanced by many recent results and it includes new applications to linear and nonlinear partial differential equations. New historical comments, five new chapters and a significantly augmented list of references aim to create a broader and modern view of the area.
Author : Kyril Tintarev
Publisher : Imperial College Press
ISBN 13 : 1860947972
Total Pages : 279 pages
Book Rating : 4.8/5 (69 download)
Download or read book Concentration Compactness written by Kyril Tintarev and published by Imperial College Press. This book was released on 2007 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concentration compactness is an important method in mathematical analysis which has been widely used in mathematical research for two decades. This unique volume fulfills the need for a source book that usefully combines a concise formulation of the method, a range of important applications to variational problems, and background material concerning manifolds, non-compact transformation groups and functional spaces. Highlighting the role in functional analysis of invariance and, in particular, of non-compact transformation groups, the book uses the same building blocks, such as partitions of domain and partitions of range, relative to transformation groups, in the proofs of energy inequalities and in the weak convergence lemmas.
Author : Nikolaos S. Papageorgiou
Publisher : Springer
ISBN 13 : 3030034305
Total Pages : 577 pages
Book Rating : 4.0/5 (3 download)
Download or read book Nonlinear Analysis - Theory and Methods written by Nikolaos S. Papageorgiou and published by Springer. This book was released on 2019-02-26 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis.
