Download or read book Fundamental Solutions and Local Solvability for Nonsmooth H rmander s Operators written by Marco Bramanti and published by . This book was released on 2017 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider operators of the form L=\sum_{i=1}^{n}X_{i}^{2}+X_{0} in a bounded domain of \mathbb{R}^{p} where X_{0},X_{1},\ldots,X_{n} are nonsmooth Hörmander's vector fields of step r such that the highest order commutators are only Hölder continuous. Applying Levi's parametrix method the authors construct a local fundamental solution \gamma for L and provide growth estimates for \gamma and its first derivatives with respect to the vector fields. Requiring the existence of one more derivative of the coefficients the authors prove that \gamma also possesses second derivatives, and the.
Download or read book Spectral Methods in MATLAB written by Lloyd N. Trefethen and published by SIAM. This book was released on 2000-07-01 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book Tools for PDE written by Michael E. Taylor and published by American Mathematical Soc.. This book was released on 2000 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developing three related tools that are useful in the analysis of partial differential equations (PDEs) arising from the classical study of singular integral operators, this text considers pseudodifferential operators, paradifferential operators, and layer potentials.
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.
Download or read book Spectra and Pseudospectra written by Lloyd N. Trefethen and published by Princeton University Press. This book was released on 2005-08-07 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.
Download or read book The Analysis of Linear Partial Differential Operators III written by Lars Hörmander and published by Springer Science & Business Media. This book was released on 2007-03-15 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "Volumes III and IV complete L. Hörmander's treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject, by the author who has dominated it and made the most significant contributions in the last decades.....It is a superb book, which must be present in every mathematical library, and an indispensable tool for all - young and old - interested in the theory of partial differential operators." L. Boutet de Monvel in Bulletin of the American Mathematical Society, 1987. "This treatise is outstanding in every respect and must be counted among the great books in mathematics. It is certainly no easy reading (...) but a careful study is extremely rewarding for its wealth of ideas and techniques and the beauty of presentation." J. Brüning in Zentralblatt MATH, 1987.
Download or read book Degenerate Elliptic Equations written by Serge Levendorskii and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first to be devoted to the study of various properties of wide classes of degenerate elliptic operators of arbitrary order and pseudo-differential operators with multiple characteristics. Conditions for operators to be Fredholm in appropriate weighted Sobolev spaces are given, a priori estimates of solutions are derived, inequalities of the Grding type are proved, and the principal term of the spectral asymptotics for self-adjoint operators is computed. A generalization of the classical Weyl formula is proposed. Some results are new, even for operators of the second order. In addition, an analogue of the Boutet de Monvel calculus is developed and the index is computed. For postgraduate and research mathematicians, physicists and engineers whose work involves the solution of partial differential equations.
Download or read book Smoothings of Piecewise Linear Manifolds written by Morris W. Hirsch and published by Princeton University Press. This book was released on 1974-10-21 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intention of the authors is to examine the relationship between piecewise linear structure and differential structure: a relationship, they assert, that can be understood as a homotopy obstruction theory, and, hence, can be studied by using the traditional techniques of algebraic topology. Thus the book attacks the problem of existence and classification (up to isotopy) of differential structures compatible with a given combinatorial structure on a manifold. The problem is completely "solved" in the sense that it is reduced to standard problems of algebraic topology. The first part of the book is purely geometrical; it proves that every smoothing of the product of a manifold M and an interval is derived from an essentially unique smoothing of M. In the second part this result is used to translate the classification of smoothings into the problem of putting a linear structure on the tangent microbundle of M. This in turn is converted to the homotopy problem of classifying maps from M into a certain space PL/O. The set of equivalence classes of smoothings on M is given a natural abelian group structure.
Download or read book Elliptic And Parabolic Equations written by Zhuoqun Wu and published by World Scientific Publishing Company. This book was released on 2006-10-17 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to elliptic and parabolic equations. While there are numerous monographs focusing separately on each kind of equations, there are very few books treating these two kinds of equations in combination. This book presents the related basic theories and methods to enable readers to appreciate the commonalities between these two kinds of equations as well as contrast the similarities and differences between them.
Download or read book Theory of Multipliers in Spaces of Differentiable Functions written by V. G. Mazʹi︠a︡ and published by Pitman Publishing. This book was released on 1985 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Linear Algebra written by Lloyd N. Trefethen and published by SIAM. This book was released on 2022-06-17 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its original appearance in 1997, Numerical Linear Algebra has been a leading textbook in its field, used in universities around the world. It is noted for its 40 lecture-sized short chapters and its clear and inviting style. It is reissued here with a new foreword by James Nagy and a new afterword by Yuji Nakatsukasa about subsequent developments.
Download or read book Differential Equations with Maple V written by Martha L Abell and published by Academic Press. This book was released on 2014-05-09 with total page 703 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Equations with Maple V provides an introduction and discussion of topics typically covered in an undergraduate course in ordinary differential equations as well as some supplementary topics such as Laplace transforms, Fourier series, and partial differential equations. It also illustrates how Maple V is used to enhance the study of differential equations not only by eliminating the computational difficulties, but also by overcoming the visual limitations associated with the solutions of differential equations. The book contains chapters that present differential equations and illustrate how Maple V can be used to solve some typical problems. The text covers topics on differential equations such as first-order ordinary differential equations, higher order differential equations, power series solutions of ordinary differential equations, the Laplace Transform, systems of ordinary differential equations, and Fourier Series and applications to partial differential equations. Applications of these topics are also provided. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful.
Download or read book Computer Methods for Mathematical Computations written by George Elmer Forsythe and published by Prentice Hall. This book was released on 1977 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Analysis and Numerical Methods for Science and Technology written by Robert Dautray and published by Springer Science & Business Media. This book was released on 1999-11-23 with total page 748 pages. Available in PDF, EPUB and Kindle. Book excerpt: These 6 volumes -- the result of a 10 year collaboration between the authors, both distinguished international figures -- compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. The advent of high-speed computers has made it possible to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way.
Download or read book One parameter Semigroups written by Edward Brian Davies and published by . This book was released on 1980 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analysis and Geometry on Groups written by Nicholas T. Varopoulos and published by Cambridge University Press. This book was released on 1993-01-07 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: The geometry and analysis that is discussed in this book extends to classical results for general discrete or Lie groups, and the methods used are analytical, but are not concerned with what is described these days as real analysis. Most of the results described in this book have a dual formulation: they have a "discrete version" related to a finitely generated discrete group and a continuous version related to a Lie group. The authors chose to center this book around Lie groups, but could easily have pushed it in several other directions as it interacts with the theory of second order partial differential operators, and probability theory, as well as with group theory.
Download or read book Elliptic Operators and Lie Groups written by Derek W. Robinson and published by . This book was released on 1991 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the basic theory of elliptic operators on Lie groups and thereby extends the conventional theory of parabolic evolution equations to a natural non-commutative context.
