Tag: Elliptic

Free Download Square Roots of Elliptic Systems in Locally Uniform Domains by Sebastian Bechtel
English | PDF EPUB (True) | 2024 | 191 Pages | ISBN : 3031637674 | 21 MB
This book establishes a comprehensive theory to treat square roots of elliptic systems incorporating mixed boundary conditions under minimal geometric assumptions. To lay the groundwork, the text begins by introducing the geometry of locally uniform domains and establishes theory for function spaces on locally uniform domains, including interpolation theory and extension operators. In these introductory parts, fundamental knowledge on function spaces, interpolation theory and geometric measure theory and fractional dimensions are recalled, making the main content of the book easier to comprehend. The centerpiece of the book is the solution to Kato’s square root problem on locally uniform domains. The Kato result is complemented by corresponding Lp bounds in natural intervals of integrability parameters.

Free Download Nonlinear Parabolic and Elliptic Equations by C. V. Pao
English | PDF | 1992 | 786 Pages | ISBN : 1461363233 | 68.7 MB
In response to the growing use of reaction diffusion problems in many fields, this monograph gives a systematic treatment of a class of nonlinear parabolic and elliptic differential equations and their applications these problems. It is an important reference for mathematicians and engineers, as well as a practical text for graduate students.

Free Download Regularity Techniques for Elliptic PDEs and the Fractional Laplacian
by Pablo Raúl Stinga
English | 2024 | ISBN: 1032679441 | 334 pages | True PDF | 9.41 MB

Free Download C*-algebras and Elliptic Theory II by Dan Burghelea, Richard Melrose, Alexander S. Mishchenko, Evgenij V. Troitsky
English | PDF (True) | 2008 | 312 Pages | ISBN : 3764386037 | 2.7 MB
This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered include the index of operators, torsion invariants, K-theory of operator algebras and L2-invariants. There are contributions from leading specialists, and the book maintains a reasonable balance between research, expository and mixed papers.

Free Download Wavelet Methods – Elliptic Boundary Value Problems and Control Problems by Angela Kunoth
English | PDF | 2001 | 150 Pages | ISBN : 3519003279 | 18.6 MB
While wavelets have since their discovery mainly been applied to problems in signal analysis and image compression, their analytic power has more and more also been recognized for problems in Numerical Analysis. Together with the functional analytic framework for different differential and integral quations, one has been able to conceptu ally discuss questions which are relevant for the fast numerical solution of such problems: preconditioning issues, derivation of stable discretizations, compression of fully popu lated matrices, evaluation of non-integer or negative norms, and adaptive refinements based on A-posteriori error estimators. This research monograph focusses on applying wavelet methods to elliptic differential equations. Particular emphasis is placed on the treatment of the boundary and the boundary conditions. Moreover, a control problem with an elliptic boundary problem as contraint serves as an example to show the conceptual strengths of wavelet techniques for some of the above mentioned issues. At this point, I would like to express my gratitude to several people before and during the process of writing this monograph. Most of all, I wish to thank Prof. Dr. Wolfgang Dahmen to whom I personally owe very much and with whom I have co-authored a large part of my work. He is responsible for the very stimulating and challenging scientific atmosphere at the Institut fiir Geometrie und Praktische Mathematik, RWTH Aachen. We also had an enjoyable collaboration with Prof. Dr. Reinhold Schneider from the Technical University of Chemnitz.