Download or read book Local Density of Solutions to Fractional Equations written by Alessandro Carbotti and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-08-19 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents in a detailed and self-contained way a new and important density result in the analysis of fractional partial differential equations, while also covering several fundamental facts about space- and time-fractional equations.
Download or read book Integro Differential Elliptic Equations written by Xavier Fernández-Real and published by Springer Nature. This book was released on 2024 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zusammenfassung: This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century. This class of equations finds relevance in fields such as analysis, probability theory, mathematical physics, and in several contexts in the applied sciences. The work gives a detailed presentation of all the necessary techniques, with a primary focus on the main ideas rather than on proving all the results in their greatest generality. The basic building blocks are presented first, with the study of the square root of the Laplacian, and weak solutions to linear equations. Subsequently, the theory of viscosity solutions to nonlinear equations is developed, and proofs are provided for the main known results in this context. The analysis finishes with the investigation of obstacle problems for integro-differential operators and establishes the regularity of solutions and free boundaries. A distinctive feature of this work lies in its presentation of nearly all covered material in a monographic format for the first time, and several proofs streamline, and often simplify, those in the original papers. Furthermore, various open problems are listed throughout the chapters
Download or read book Contemporary Research in Elliptic PDEs and Related Topics written by Serena Dipierro and published by Springer. This book was released on 2019-07-12 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017. The contributions cover several aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applications. The topics covered include nonlocal equations, elliptic equations and systems, fully nonlinear equations, nonlinear parabolic equations, overdetermined boundary value problems, maximum principles, geometric analysis, control theory, mean field games, and bio-mathematics. The authors are trailblazers in these topics and present their work in a way that is exhaustive and clearly accessible to PhD students and early career researcher. As such, the book offers an excellent introduction to a variety of fundamental topics of contemporary investigation and inspires novel and high-quality research.
Download or read book Time Frequency Analysis of Operators written by Elena Cordero and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-09-21 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative text studies pseudodifferential and Fourier integral operators in the framework of time-frequency analysis, providing an elementary approach, along with applications to almost diagonalization of such operators and to the sparsity of their Gabor representations. Moreover, Gabor frames and modulation spaces are employed to study dispersive equations such as the Schrödinger, wave, and heat equations and related Strichartz problems. The first part of the book is addressed to non-experts, presenting the basics of time-frequency analysis: short time Fourier transform, Wigner distribution and other representations, function spaces and frames theory, and it can be read independently as a short text-book on this topic from graduate and under-graduate students, or scholars in other disciplines.
Download or read book The Structure of Compact Groups written by Karl H. Hofmann and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-06-08 with total page 1398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed both as a textbook for high-level graduate courses and as a reference for researchers who need to apply the structure and representation theory of compact groups. A gentle introduction to compact groups and their representation theory is followed by self-contained courses on linear and compact Lie groups, and on locally compact abelian groups. This fourth edition was updated with the latest developments in the field.
Download or read book Formal Analysis written by Xiao-Xiong Gan and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-06-08 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Formal analysis is the study of formal power series, formal Laurent series, formal root series, and other formal series or formal functionals. This book is the first comprehensive presentation of the topic that systematically introduces formal analysis, including its algebraic, analytic, and topological structure, along with various applications.
Download or read book Ulrich Bundles written by Laura Costa and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-05-10 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to cover the active developments of arithmetically Cohen-Macaulay and Ulrich bundles and related topics in the last 30 years, and to present relevant techniques and multiple applications of the theory of Ulrich bundles to a wide range of problems in algebraic geometry as well as in commutative algebra.
Download or read book Symmetry and Exact Solutions of Nonlinear Mathematical Physics Equations written by Gangwei Wang and published by Frontiers Media SA. This book was released on 2024-08-13 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear problems, originating from applied science that is closely related to practices, contain rich and extensive content. It makes the corresponding nonlinear models also complex and diverse. Due to the intricacy and contingency of nonlinear problems, unified mathematical methods still remain far and few between. In this regard, the comprehensive use of symmetric methods, along with other mathematical methods, becomes an effective option to solve nonlinear problems.
Download or read book NASA Technical Report written by and published by . This book was released on 1961 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Partial Differential Equations and Geometric Measure Theory written by Alessio Figalli and published by Springer. This book was released on 2018-05-23 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas and variational methods. The problems addressed are challenging and complex, and often require the use of several refined techniques to overcome the major difficulties encountered. The lectures, given during the course "Partial Differential Equations and Geometric Measure Theory'' in Cetraro, June 2–7, 2014, should help to encourage further research in the area. The enthusiasm of the speakers and the participants of this CIME course is reflected in the text.
Download or read book General Fractional Derivatives with Applications in Viscoelasticity written by Xiao-Jun Yang and published by Academic Press. This book was released on 2020-04-03 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: General Fractional Derivatives with Applications in Viscoelasticity introduces the newly established fractional-order calculus operators involving singular and non-singular kernels with applications to fractional-order viscoelastic models from the calculus operator viewpoint. Fractional calculus and its applications have gained considerable popularity and importance because of their applicability to many seemingly diverse and widespread fields in science and engineering. Many operations in physics and engineering can be defined accurately by using fractional derivatives to model complex phenomena. Viscoelasticity is chief among them, as the general fractional calculus approach to viscoelasticity has evolved as an empirical method of describing the properties of viscoelastic materials. General Fractional Derivatives with Applications in Viscoelasticity makes a concise presentation of general fractional calculus. - Presents a comprehensive overview of the fractional derivatives and their applications in viscoelasticity - Provides help in handling the power-law functions - Introduces and explores the questions about general fractional derivatives and its applications
Download or read book Shielding of Partially Reflecting Stagnation Surfaces Against Radiation by Transpiration of an Absorbing Gas written by John Thomas Howe and published by . This book was released on 1961 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: The laminar compressible boundary layer in the two dimensional and axisymmetric stagnation regions has been analyzed to show the effects of the injection of a radiation absorbing gas on the incident radiation field, on enthalpy profiles, and on heat transfer to the vehicle surface. Heat-transfer results are presented and are compared with those for the unshielded case. The required absorption properties of the foreign gas are determined and compared with properties of known gases.
Download or read book Thermodynamics of Solutions written by Eli Ruckenstein and published by Springer Science & Business Media. This book was released on 2009-06-17 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of a number of papers regarding the thermodynamics and structure of multicomponent systems that we have published during the last decade. Even though they involve different topics and different systems, they have something in common which can be considered as the “signature” of the present book. First, these papers are concerned with “difficult” or very nonideal systems, i. e. systems with very strong interactions (e. g. , hyd- gen bonding) between components or systems with large differences in the partial molar v- umes of the components (e. g. , the aqueous solutions of proteins), or systems that are far from “normal” conditions (e. g. , critical or near-critical mixtures). Second, the conventional th- modynamic methods are not sufficient for the accurate treatment of these mixtures. Last but not least, these systems are of interest for the pharmaceutical, biomedical, and related ind- tries. In order to meet the thermodynamic challenges involved in these complex mixtures, we employed a variety of traditional methods but also new methods, such as the fluctuation t- ory of Kirkwood and Buff and ab initio quantum mechanical techniques. The Kirkwood-Buff (KB) theory is a rigorous formalism which is free of any of the - proximations usually used in the thermodynamic treatment of multicomponent systems. This theory appears to be very fruitful when applied to the above mentioned “difficult” systems.
Download or read book Principles of Physical Cosmology written by P. J. E. Peebles and published by Princeton University Press. This book was released on 2020-09-15 with total page 751 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classic introduction to physical cosmology from Nobel Prize–winning physicist P. J. E. Peebles Principles of Physical Cosmology is the essential introduction to this critical area of modern physics, written by a leading pioneer who has shaped the course of the field for decades. P. J. E. Peebles provides an authoritative overview of the field, showing how observation has combined with theory to establish the science of physical cosmology. He presents the elements of physical cosmology, including the history of the discovery of the expanding universe; surveys the cosmological tests that measure the geometry of space-time, with a discussion of general relativity as the basis for these tests; and reviews the origin of galaxies and the large-scale structure of the universe. Now featuring Peebles's 2019 Nobel lecture, Principles of Physical Cosmology remains an indispensable reference for students and researchers alike.
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 165 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.
Download or read book Elliptic and Parabolic Equations Involving the Hardy Leray Potential written by Ireneo Peral Alonso and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-02-22 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: The scientific literature on the Hardy-Leray inequality, also known as the uncertainty principle, is very extensive and scattered. The Hardy-Leray potential shows an extreme spectral behavior and a peculiar influence on diffusion problems, both stationary and evolutionary. In this book, a big part of the scattered knowledge about these different behaviors is collected in a unified and comprehensive presentation.
Download or read book Ergodicity for Infinite Dimensional Systems written by Giuseppe Da Prato and published by Cambridge University Press. This book was released on 1996-05-16 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the only book on stochastic modelling of infinite dimensional dynamical systems.
