eBook PDF Download Digital Library
Author: Juha Heinonen
Publisher: Courier Dover Publications
Published: 2018-05-16
Total Pages: 416
ISBN-13: 0486830462
DOWNLOAD EBOOK →A self-contained treatment appropriate for advanced undergraduates and graduate students, this text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. 1993 edition.
Author: Bengt O. Turesson
Publisher: Springer
Published: 2007-05-06
Total Pages: 188
ISBN-13: 3540451684
DOWNLOAD EBOOK →The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems.
Author: Josef Kral
Publisher: Walter de Gruyter
Published: 2011-10-13
Total Pages: 513
ISBN-13: 3110818574
DOWNLOAD EBOOK →The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Author: Olli Martio
Publisher: Springer Science & Business Media
Published: 2008-11-09
Total Pages: 368
ISBN-13: 0387855882
DOWNLOAD EBOOK →Based on recent research papers, this book presents a modern account of mapping theory with emphasis on quasiconformal mapping and its generalizations. It contains an extensive bibliography.
Author: Vladimir Maz'ya
Publisher: Springer Science & Business Media
Published: 2008-12-02
Total Pages: 395
ISBN-13: 038785648X
DOWNLOAD EBOOK →This volume mark’s the centenary of the birth of the outstanding mathematician of the 20th century, Sergey Sobolev. It includes new results on the latest topics of the theory of Sobolev spaces, partial differential equations, analysis and mathematical physics.
Author: Marco Biroli
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 184
ISBN-13: 9401100853
DOWNLOAD EBOOK →Recent years have witnessed an increasingly close relationship growing between potential theory, probability and degenerate partial differential operators. The theory of Dirichlet (Markovian) forms on an abstract finite or infinite-dimensional space is common to all three disciplines. This is a fascinating and important subject, central to many of the contributions to the conference on `Potential Theory and Degenerate Partial Differential Operators', held in Parma, Italy, February 1994.
Author: J. Kral
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 138
ISBN-13: 1461344255
DOWNLOAD EBOOK →Preface.- Gottfried Anger: Direct and inverse problems in potential theory.- Viorel Barbu: Regularity results for sane differential equations associated with maximal monotone operators in Hilbert spaces.- Haim Brezis: Classes d'interpolation associées à un opérateur monotone et applications.- Siegfried Dnümmel: On inverse problems for k-dimensional potentials.- Jozef Ka?ur: Application of Rothe's method to nonlinear parabolic boundary value problems.- Josef Král: Potentials and removability of singularities.- Vladimir Lovicar: Theorem of Fréchet and asymptotically almost periodid solutions of.
Author: Jan Malý
Publisher: American Mathematical Soc.
Published: 1997
Total Pages: 309
ISBN-13: 0821803352
DOWNLOAD EBOOK →The primary objective of this monograph is to give a comprehensive exposition of results surrounding the work of the authors concerning boundary regularity of weak solutions of second order elliptic quasilinear equations in divergence form. The book also contains a complete development of regularity of solutions of variational inequalities, including the double obstacle problem, where the obstacles are allowed to be discontinuous. The book concludes with a chapter devoted to the existence theory thus providing the reader with a complete treatment of the subject ranging from regularity of weak solutions to the existence of weak solutions.
Author: Albo Carlos Cavalheiro
Publisher: Cambridge Scholars Publishing
Published: 2023-09-29
Total Pages: 333
ISBN-13: 1527551679
DOWNLOAD EBOOK →In various applications, we can meet boundary value problems for elliptic equations whose ellipticity is disturbed in the sense that some degeneration or singularity appears. This bad behavior can be caused by the coefficients of the corresponding differential operator as well as by the solution itself. There are several very concrete problems in various practices which lead to such differential equations, such as glaciology, non-Newtonian fluid mechanics, flows through porous media, differential geometry, celestial mechanics, climatology, and reaction-diffusion problems, among others. This book is based on research by the author on degenerate elliptic equations. This book will be a useful reference source for graduate students and researchers interested in differential equations.
Author: Veron Laurent
Publisher: World Scientific
Published: 2017-05-05
Total Pages: 476
ISBN-13: 9814730343
DOWNLOAD EBOOK →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.
