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Books on the topic 'Degenerate elliptic equation'

Author: Grafiati

Published: 11 March 2023

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1

Levendorskii, Serge. Degenerate Elliptic Equations. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-1215-6.

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2

Levendorskiĭ, Serge. Degenerate elliptic equations. Dordrecht: Kluwer, 1993.

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3

Tero, Kilpeläinen, and Martio O, eds. Nonlinear potential theory of degenerate elliptic equations. Oxford: Clarendon Press, 1993.

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4

A, Dzhuraev. Degenerate and other problems. Harlow, Essex, England: Longman Scientific and Technical, 1992.

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5

On first and second order planar elliptic equations with degeneracies. Providence, R.I: American Mathematical Society, 2011.

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6

Colombo, Maria. Flows of Non-smooth Vector Fields and Degenerate Elliptic Equations. Pisa: Scuola Normale Superiore, 2017. http://dx.doi.org/10.1007/978-88-7642-607-0.

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7

Popivanov, Peter R. The degenerate oblique derivative problem for elliptic and parabolic equations. Berlin: Akademie Verlag, 1997.

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8

Elliptic, hyperbolic and mixed complex equations with parabolic degeneracy. Singapore: World Scientific, 2008.

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9

Colombo, Maria. Flows of Non-smooth Vector Fields and Degenerate Elliptic Equations: With Applications to the Vlasov-Poisson and Semigeostrophic Systems. Pisa: Scuola Normale Superiore, 2017.

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10

1943-, Gossez J. P., and Bonheure Denis, eds. Nonlinear elliptic partial differential equations: Workshop in celebration of Jean-Pierre Gossez's 65th birthday, September 2-4, 2009, Université libre de Bruxelles, Belgium. Providence, R.I: American Mathematical Society, 2011.

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11

Degenerate Elliptic Equations. Springer, 2010.

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12

Levendorskii, Serge. Degenerate Elliptic Equations. Springer, 2013.

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13

Nonlinear Potential Theory of Degenerate Elliptic Equations. Dover Publications, 2006.

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14

Martio, Olli, Juha Heinonen, and Tero Kipelainen. Nonlinear Potential Theory of Degenerate Elliptic Equations. Dover Publications, Incorporated, 2018.

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15

Kilpelainen, Tero, Olli Martio, and Juha Heinonen. Nonlinear Potential Theory of Degenerate Elliptic Equations. Dover Publications, Incorporated, 2012.

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16

Martio, Olli, Juha Heinonen, and Tero Kipelainen. Nonlinear Potential Theory of Degenerate Elliptic Equations. Dover Publications, Incorporated, 2018.

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17

Stredulinsky, E. W. Weighted Inequalities and Degenerate Elliptic Partial Differential Equations. Springer London, Limited, 2006.

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18

Veron, Laurent. Local and Global Aspects of Quasilinear Degenerate Elliptic Equations. World Scientific Publishing Co Pte Ltd, 2017.

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19

Epstein, Charles L., and Rafe Mazzeo. Degenerate Diffusion Operators Arising in Population Biology (AM-185). Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.001.0001.

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This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the martingale problem and therefore the existence of the associated Markov process. The book uses an “integral kernel method” to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. The book establishes the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. It shows that the semigroups defined by these operators have holomorphic extensions to the right half plane. The book also demonstrates precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.

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20

Epstein, Charles L., and Rafe Mazzeo. Introduction. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0001.

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This book proves the existence, uniqueness and regularity results for a class of degenerate elliptic operators known as generalized Kimura diffusions, which act on functions defined on manifolds with corners. It presents a generalization of the Hopf boundary point maximum principle that demonstrates, in the general case, how regularity implies uniqueness. The book is divided in three parts. Part I deals with Wright–Fisher geometry and the maximum principle; Part II is devoted to an analysis of model problems, and includes degenerate Hölder spaces; and Part III discusses generalized Kimura diffusions. This introductory chapter provides an overview of generalized Kimura diffusions and their applications in probability theory, model problems, perturbation theory, main results, and alternate approaches to the study of similar degenerate elliptic and parabolic equations.

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21

Palagachev, Dian K., and Peter R. Popivanov. The Degenerate Oblique Derivative Problem for Elliptic and Parabolic Equations (Mathematical Research (Akademie Verlag), Vol 93). John Wiley & Sons Ltd (Import), 1998.

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22

Korobenko, Lyudmila, Cristian Rios, Eric Sawyer, and Ruipeng Shen. Local Boundedness, Maximum Principles, and Continuity of Solutions to Infinitely Degenerate Elliptic Equations with Rough Coefficients. American Mathematical Society, 2021.

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23

Colombo, Maria. Flows of Non-Smooth Vector Fields and Degenerate Elliptic Equations: With Applications to the Vlasov-Poisson and Semigeostrophic Systems. Edizioni della Normale, 2018.

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