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.
Автор: Maurizio Garrione; Filippo Gazzola Название: Nonlinear Equations for Beams and Degenerate Plates with Piers ISBN: 3030302172 ISBN-13(EAN): 9783030302177 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book develops a full theory for hinged beams and degenerate plates with multiple intermediate piers with the final purpose of understanding the stability of suspension bridges. New models are proposed and new tools are provided for the stability analysis. The book opens by deriving the PDE’s based on the physical models and by introducing the basic framework for the linear stationary problem. The linear analysis, in particular the behavior of the eigenvalues as the position of the piers varies, enables the authors to tackle the stability issue for some nonlinear evolution beam equations, with the aim of determining the “best position” of the piers within the beam in order to maximize its stability. The study continues with the analysis of a class of degenerate plate models. The torsional instability of the structure is investigated, and again, the optimal position of the piers in terms of stability is discussed. The stability analysis is carried out by means of both analytical tools and numerical experiments. Several open problems and possible future developments are presented. The qualitative analysis provided in the book should be seen as the starting point for a precise quantitative study of more complete models, taking into account the action of aerodynamic forces. This book is intended for a two-fold audience. It is addressed both to mathematicians working in the field of Differential Equations, Nonlinear Analysis and Mathematical Physics, due to the rich number of challenging mathematical questions which are discussed and left as open problems, and to Engineers interested in mechanical structures, since it provides the theoretical basis to deal with models for the dynamics of suspension bridges with intermediate piers. More generally, it may be enjoyable for readers who are interested in the application of Mathematics to real life problems.
Автор: Anne-Laure Dalibard, Laure Saint-Raymond Название: Mathematical Study of Degenerate Boundary Layers: A Large Scale Ocean Circulation Problem ISBN: 1470428350 ISBN-13(EAN): 9781470428358 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 77610.00 T Наличие на складе: Невозможна поставка. Описание: Offers a complete asymptotic analysis as $E \to 0$ of the Munk equation $\partial _x\psi -E \Delta ^2 \psi = \tau $ in a domain $\Omega \subset \mathbf R^2$, supplemented with boundary conditions for $\psi $ and $\partial _n \psi $. This equation is a simple model for the circulation of currents in closed basins, the variables $x$ and $y$ being respectively the longitude and the latitude.
Автор: P. Cannarsa, P. Martinez, J. Vancostenoble Название: Global Carleman Estimates for Degenerate Parabolic Operators with Applications ISBN: 1470414961 ISBN-13(EAN): 9781470414962 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 99790.00 T Наличие на складе: Невозможна поставка. Описание: Introduces the reader to global Carleman estimates for a class of parabolic operators which may degenerate at the boundary of the space domain, in the normal direction to the boundary. Such a kind of degeneracy is relevant to study the invariance of a domain with respect to a given stochastic diffusion flow, and appears naturally in climatology models.
Автор: Wei-Ming Ni; L.A. Peletier; J.L. Vazquez Название: Degenerate Diffusions ISBN: 1461269350 ISBN-13(EAN): 9781461269359 Издательство: Springer Рейтинг: Цена: 93160.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This IMA Volume in Mathematics and its Applications DEGENERATE DIFFUSIONS is based on the proceedings of a workshop which was an integral part of the 1990- 91 IMA program on "Phase Transitions and Free Boundaries".
Автор: Wei-Ming Ni; L.A. Peletier; J.L. Vazquez Название: Degenerate Diffusions ISBN: 0387940685 ISBN-13(EAN): 9780387940687 Издательство: Springer Рейтинг: Цена: 167700.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This IMA Volume in Mathematics and its Applications DEGENERATE DIFFUSIONS is based on the proceedings of a workshop which was an integral part of the 1990- 91 IMA program on "Phase Transitions and Free Boundaries".
Автор: Serge Levendorskii Название: Degenerate Elliptic Equations ISBN: 079232305X ISBN-13(EAN): 9780792323051 Издательство: Springer Рейтинг: Цена: 102480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: A study of the 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, and a priori estimates of solutions are derived.
Автор: Maria Colombo Название: Flows of Non-Smooth Vector Fields and Degenerate Elliptic Equations ISBN: 887642606X ISBN-13(EAN): 9788876426063 Издательство: Springer Рейтинг: Цена: 16770.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This text represents a sort of customary or ordinal for the English court chapel in 1449, intended to govern the life of the 49 people, including choirboys, who were the staff of this peripatetic establishment. It was based on earlier drafts, and was sent to Alvaro Vaz d`Almada, a knight of the Garter, for the use of Afonso V of Portugal; it includes a copy of the English coronation rites.
Автор: Marco Biroli Название: Potential Theory and Degenerate Partial Differential Operators ISBN: 0792335961 ISBN-13(EAN): 9780792335962 Издательство: Springer Рейтинг: Цена: 119210.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This work discusses the blending of potential theory, probability and degenerate partial differential operators. The theory of Dirichlet (Markovian) which forms on an abstract finite or infinite-dimensional space is common to all three disciplines and is investigated here.
Автор: Fragnelli Genni, Mugnai Dimitri Название: Control of Degenerate and Singular Parabolic Equations: Carleman Estimates and Observability ISBN: 3030693481 ISBN-13(EAN): 9783030693480 Издательство: Springer Цена: 60550.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book collects some basic results on the null controllability for degenerate and singular parabolic problems. For these reasons, the authors will not give all the detailed proofs of the given theorems, but just some of them, in order to show the underlying strategy in this area.
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