Local Boundedness, Maximum Principles, and Continuity of Solutions to Infinitely Degenerate Elliptic Equations with Rough Coefficients PDF Download

Author: Lyudmila Korobenko
Publisher: American Mathematical Soc.
ISBN: 1470444011
Category : Education
Languages : en
Pages : 130

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View the abstract: https://bookstore.ams.org/memo-269-1311/

Author: Serge Levendorskii
Publisher: Springer Science & Business Media
ISBN: 9401712158
Category : Mathematics
Languages : en
Pages : 442

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Book Description
This volume is the first to be devoted to the study of various 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, a priori estimates of solutions are derived, inequalities of the Grding type are proved, and the principal term of the spectral asymptotics for self-adjoint operators is computed. A generalization of the classical Weyl formula is proposed. Some results are new, even for operators of the second order. In addition, an analogue of the Boutet de Monvel calculus is developed and the index is computed. For postgraduate and research mathematicians, physicists and engineers whose work involves the solution of partial differential equations.

Author: Marco Biroli
Publisher: Springer Science & Business Media
ISBN: 9401100853
Category : Mathematics
Languages : en
Pages : 184

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Book Description
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: Laurent Veron
Publisher: World Scientific
ISBN: 9814730343
Category : Mathematics
Languages : en
Pages : 474

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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:

Author: Duván Cardona
Publisher: Springer Nature
ISBN: 3031485793
Category :
Languages : en
Pages : 262

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Author: Albo Carlos Cavalheiro
Publisher: Cambridge Scholars Publishing
ISBN: 1527551679
Category : Mathematics
Languages : en
Pages : 333

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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: Unione matematica italiana
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 554

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Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 652

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Author: C.M. Dafermos
Publisher: Elsevier
ISBN: 0080521827
Category : Mathematics
Languages : en
Pages : 579

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This book contains several introductory texts concerning the main directions in the theory of evolutionary partial differential equations. The main objective is to present clear, rigorous,and in depth surveys on the most important aspects of the present theory. The table of contents includes: W.Arendt: Semigroups and evolution equations: Calculus, regularity and kernel estimatesA.Bressan: The front tracking method for systems of conservation lawsE.DiBenedetto, J.M.Urbano,V.Vespri: Current issues on singular and degenerate evolution equations;L.Hsiao, S.Jiang: Nonlinear hyperbolic-parabolic coupled systemsA.Lunardi: Nonlinear parabolic equations and systemsD.Serre:L1-stability of nonlinear waves in scalar conservation laws B.Perthame:Kinetic formulations of parabolic and hyperbolic PDE's: from theory to numerics

Author: Maria Colombo
Publisher: Springer
ISBN: 8876426078
Category : Mathematics
Languages : en
Pages : 285

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Book Description
The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows.​