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: Genni Fragnelli, Dimitri Mugnai Название: Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations ISBN: 1470419548 ISBN-13(EAN): 9781470419547 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 72990.00 T Наличие на складе: Невозможна поставка. Описание: The authors consider a parabolic problem with degeneracy in the interior of the spatial domain, and they focus on observability results through Carleman estimates for the associated adjoint problem. The novelties of the present paper are two. First, the coefficient of the leading operator only belongs to a Sobolev space. Second, the degeneracy point is allowed to lie even in the interior of the control region, so that no previous result can be adapted to this situation; however, different cases can be handled, and new controllability results are established as a consequence.
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: 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: Emmanuele DiBenedetto; Prof. Ugo Pietro Gianazza U Название: Harnack`s Inequality for Degenerate and Singular Parabolic Equations ISBN: 1489999760 ISBN-13(EAN): 9781489999764 Издательство: Springer Рейтинг: Цена: 111790.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years. Despite important achievements, the issue of the Harnack inequality for non-negative solutions to these equations, both of p-Laplacian and porous medium type, while raised by several authors, has remained basically open. Recently considerable progress has been made on this issue, to the point that, except for the singular sub-critical range, both for the p-laplacian and the porous medium equations, the theory is reasonably complete.
It seemed therefore timely to trace a comprehensive overview, that would highlight the main issues and also the problems that still remain open. The authors give a comprehensive treatment of the Harnack inequality for non-negative solutions to p-laplace and porous medium type equations, both in the degenerate (p>2 or m>1) and in the singular range (1pmThe book is self-contained. Building on a similar monograph by the first author, the authors of the present book focus entirely on the Harnack estimates and on their applications: indeed a number of known regularity results are given a new proof, based on the Harnack inequality. It is addressed to all professionals active in the field, and also to advanced graduate students, interested in understanding the main issues of this fascinating research field.
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: 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: 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: Dzhuraev, Abduhamid Название: Degenerate and Other Problems ISBN: 036745016X ISBN-13(EAN): 9780367450168 Издательство: Taylor&Francis Рейтинг: Цена: 63280.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book contains a collection of problems, including boundary-value problems for elliptic systems and initial-boundary-value problems for hyperbolic systems, arising in partial differential equations investigated by means of complex analysis approached in elementary ways.
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.
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