Parabolic Equations with Irregular Data and Related Issues: Applications to Stochastic Differential Equations, Claude Le Bris, Pierre-Louis Lions

Автор: Ahmad Shair
Название: Textbook on Ordinary Differential Equations
ISBN: 3319164074 ISBN-13(EAN): 9783319164076
Издательство: Springer
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Цена: 46570.00 T
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Описание: The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics. A complete Solutions Manual, containing solutions to all the exercises published in the book, is available.

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)
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Цена: 99790.00 T
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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: Alexander A. Kovalevsky, Igor I. Skrypnik, Andrey E. Shishkov
Название: Singular Solutions of Nonlinear Elliptic and Parabolic Equations
ISBN: 3110315483 ISBN-13(EAN): 9783110315486
Издательство: Walter de Gruyter
Цена: 223090.00 T
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Описание: This monograph looks at several trends in the investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions for elliptic second-order equations and some classes of fourth-order equations with L1-data and questions on the removability of singularities of solutions to elliptic and parabolic second-order equations in divergence form. It looks at localized and nonlocalized singularly peaking boundary regimes for different classes of quasilinear parabolic second- and high-order equations in divergence form.The book will be useful for researchers and post-graduate students that specialize in the field of the theory of partial differential equations and nonlinear analysis.Contents:ForewordPart I: Nonlinear elliptic equations with L^1-dataNonlinear elliptic equations of the second order with L^1-dataNonlinear equations of the fourth order with strengthened coercivity and L^1-dataPart II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second orderRemovability of singularities of the solutions of quasilinear elliptic equationsRemovability of singularities of the solutions of quasilinear parabolic equationsQuasilinear elliptic equations with coefficients from the Kato classPart III: Boundary regimes with peaking for quasilinear parabolic equationsEnergy methods for the investigation of localized regimes with peaking for parabolic second-order equationsMethod of functional inequalities in peaking regimes for parabolic equations of higher ordersNonlocalized regimes with singular peakingAppendix: Formulations and proofs of the auxiliary resultsBibliography

Автор: Kashiwara
Название: Regular and Irregular Holonomic D-Modules
ISBN: 1316613453 ISBN-13(EAN): 9781316613450
Издательство: Cambridge Academ
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Цена: 55970.00 T
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Описание: The theory of D-modules applies to many areas, including linear PDEs, group representation, algebraic geometry and mathematical physics. This book is the first devoted specifically to the most important variety, holonomic D-modules. It provides a complete unified treatment of the theory of holonomic D-modules, both regular and irregular.

Автор: VIOREL BARBU
Название: Controllability and Stabilization of Parabolic Equations
ISBN: 3319766651 ISBN-13(EAN): 9783319766652
Издательство: Springer
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Цена: 93160.00 T
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Описание: This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems.

Автор: Gershon Kresin, Vladimir Maz`ya
Название: Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems
ISBN: 0821889818 ISBN-13(EAN): 9780821889817
Издательство: Mare Nostrum (Eurospan)
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Цена: 96090.00 T
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Описание: The main goal of this book is to present results pertaining to various versions of the maximum principle for elliptic and parabolic systems of arbitrary order. In particular, the authors present necessary and sufficient conditions for validity of the classical maximum modulus principles for systems of second order and obtain sharp constants in inequalities of Miranda-Agmon type and in many other inequalities of a similar nature. Somewhat related to this topic are explicit formulas for the norms and the essential norms of boundary integral operators. The proofs are based on a unified approach using, on one hand, representations of the norms of matrix-valued integral operators whose target spaces are linear and finite dimensional, and, on the other hand, on solving certain finite dimensional optimization problems. This book reflects results obtained by the authors, and can be useful to research mathematicians and graduate students interested in partial differential equations.

Автор: Atsushi Yagi
Название: Abstract Parabolic Evolution Equations and their Applications
ISBN: 3642261795 ISBN-13(EAN): 9783642261794
Издательство: Springer
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Цена: 102480.00 T
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Описание: This book offers an overview of the theories of linear, semilinear and quasilinear abstract parabolic evolution equations. It also shows how to apply the abstract results to various models in the real world focusing on various self-organization models.

Автор: Donatella Danielli, Nicola Garofalo, Arshak Petrosyan, Tung To
Название: Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem
ISBN: 1470425475 ISBN-13(EAN): 9781470425470
Издательство: Mare Nostrum (Eurospan)
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Цена: 74850.00 T
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Описание: Offers a comprehensive treatment of the parabolic Signorini problem based on a generalization of Almgren`s monotonicity of the frequency. This includes the proof of the optimal regularity of solutions, classification of free boundary points, the regularity of the regular set and the structure of the singular set.

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)
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Цена: 72990.00 T
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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: N.V. Krylov
Название: Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations
ISBN: 1470447401 ISBN-13(EAN): 9781470447403
Издательство: Mare Nostrum (Eurospan)
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Цена: 107850.00 T
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Описание: This book concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. We look for solutions in Sobolev classes, local or global, or for viscosity solutions. Most of the auxiliary results, such as Aleksandrov's elliptic and parabolic estimates, the Krylov-Safonov and the Evans-Krylov theorems, are taken from old sources, and the main results were obtained in the last few years.Presentation of these results is based on a generalization of the Fefferman-Stein theorem, on Fang-Hua Lin's like estimates, and on the so-called ``ersatz'' existence theorems, saying that one can slightly modify ``any'' equation and get a ``cut-off'' equation that has solutions with bounded derivatives. These theorems allow us to prove the solvability in Sobolev classes for equations that are quite far from the ones which are convex or concave with respect to the Hessians of the unknown functions. In studying viscosity solutions, these theorems also allow us to deal with classical approximating solutions, thus avoiding sometimes heavy constructions from the usual theory of viscosity solutions.