Local and Global Aspects of Quasilinear Degenerate Elliptic Equations
Local and Global Aspects of Quasilinear Degenerate Elliptic Equations

Author: Laurent Veron

Publisher: World Scientific Publishing Company

Published: 2016-09-30

Total Pages: 457

ISBN-13: 9789814730327

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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.

Quasilinear Elliptic Equations with Degenerations and Singularities
Quasilinear Elliptic Equations with Degenerations and Singularities

Author: Pavel Drábek

Publisher: Walter de Gruyter

Published: 1997

Total Pages: 240

ISBN-13: 9783110154900

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The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-Chief J rgen Appell, W rzburg, Germany Honorary and Advisory Editors Catherine Bandle, Basel, Switzerland Alain Bensoussan, Richardson, Texas, USA Avner Friedman, Columbus, Ohio, USA Umberto Mosco, Worcester, Massachusetts, USA Louis Nirenberg, New York, USA Alfonso Vignoli, Rome, Italy Editorial Board Manuel del Pino, Bath, UK, and Santiago, Chile Mikio Kato, Nagano, Japan Wojciech Kryszewski, Toruń, Poland Vicenţiu D. Rădulescu, Krak w, Poland Simeon Reich, Haifa, Israel Please submit book proposals to J rgen Appell. Titles in planning include Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019) Tomasz W. Dlotko and Yejuan Wang, Critical Parabolic-Type Problems (2019) Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019) Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy-Leray Potential (2020) Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020) Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)