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Books on the topic 'Degenerate equation'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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1

Wakako, Hideaki. Exact WKB analysis for the degenerate third Painleve equation of type (Ds). Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2007.

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2

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

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DiBenedetto, Emmanuele. Degenerate Parabolic Equations. Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0895-2.

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4

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

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DiBenedetto, Emmanuele. Degenerate parabolic equations. Springer-Verlag, 1993.

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6

Favini, Angelo, and Gabriela Marinoschi. Degenerate Nonlinear Diffusion Equations. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28285-0.

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7

Favini, Angelo. Degenerate Nonlinear Diffusion Equations. Springer Berlin Heidelberg, 2012.

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8

A, Dzhuraev. Degenerate and other problems. Longman Scientific and Technical, 1992.

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9

Ahmed, Zeriahi, ed. Degenerate complex Monge--Ampère equations. European Mathematical Society Publishing House, 2017.

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10

Favini, A. Degenerate differential equations in Banach spaces. Marcel Dekker, 1999.

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11

-M, Ni W., Peletier L. A, and Vazquez J. L, eds. Degenerate diffusions. Springer-Verlag, 1993.

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12

Bell, Denis R. Degenerate stochastic differential equations and hypoellipticity. Longman, 1995.

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13

Bell, Denis R. Degenerate stochastic differential equations and hypoellipticity. Longman, 1995.

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14

Fragnelli, Genni, and Dimitri Mugnai. Control of Degenerate and Singular Parabolic Equations. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69349-7.

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15

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

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16

DiBenedetto, Emmanuele, Ugo Gianazza, and Vincenzo Vespri. Harnack's Inequality for Degenerate and Singular Parabolic Equations. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-1584-8.

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17

Ugo, Gianazza, Vespri Vincenzo, and SpringerLink (Online service), eds. Harnack's Inequality for Degenerate and Singular Parabolic Equations. Springer Science+Business Media, LLC, 2012.

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18

Garrione, Maurizio, and Filippo Gazzola. Nonlinear Equations for Beams and Degenerate Plates with Piers. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-30218-4.

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19

Sviridyuk, G. A. Linear Sobolev type equations and degenerate semigroups of operators. VSP, 2003.

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20

Arutyunov, Aram V. Optimality Conditions: Abnormal and Degenerate Problems. Springer Netherlands, 2000.

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21

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

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22

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

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23

1953-, Kenig Carlos E., ed. Degenerate diffusions: Initial value problems and local regularity theory. European Mathematical Society, 2007.

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24

Watling, Keith Duncan. Formulae for solutions to (possibly degenerate) diffusion equations exhibiting semi-classical and small time asymptotics. typescript, 1986.

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25

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

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26

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. American Mathematical Society, 2011.

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27

Balackiy, Evgeniy, Natal'ya Ekimova, Aleksandr Rudnev, and Aleksandr Gusev. New approaches to modeling economic development. INFRA-M Academic Publishing LLC., 2022. http://dx.doi.org/10.12737/1862597.

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The monograph presents new results of the authors' long-term research on various topical issues of economic development. All the proposed new approaches are given in the broad context of already existing theories and models, as well as illustrated by numerous vivid examples from the history of different countries. Most of the topics covered belong to the category of the most burning social issues of our time, which gives the work an element of scientific "freshness" and discussion. All the fundamental theses are accompanied by the necessary models, equations, formulas, graphs and figures, but

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28

DiBenedetto, Emmanuele. Degenerate Parabolic Equations. Springer, 2012.

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29

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

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30

Degenerate Elliptic Equations. Springer, 2010.

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31

Degenerate Nonlinear Diffusion Equations. Springer, 2012.

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32

Saha, Prasenjit, and Paul A. Taylor. Gravity versus Pressure. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198816461.003.0005.

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Formally, the title of this chapter is a statement of the equation of hydrostatic equilibrium. A large number of stellar objects exist in the balance between gravity and pressure, with the large ‘zoo’ of observed types being due to the various physical phenomena providing the latter. This chapter is devoted to various applications of that equilibrium. Some cases can be solved exactly, such as spheres of solid rock or ice; some cases can only be solved in detail numerically, notably degenerate white dwarfs up to the Chandrasekhar mass limit. For other cases, analytical approximations such as a

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33

Favini, Angelo, and Atsushi Yagi. Degenerate Differential Equations in Banach Spaces. Taylor & Francis Group, 1998.

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34

Degenerate Differential Equations in Banach Spaces. Taylor & Francis Group, 1998.

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35

Attractors for Degenerate Parabolic Type Equations. American Mathematical Society, 2013.

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36

Bell, Denis. Degenerate Stochastic Differential Equations and Hypoellipticity. Taylor & Francis Group, 1996.

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37

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

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38

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

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39

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

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40

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

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41

Borodin, Alexei, and Leonid Petrov. Integrable probability: stochastic vertex models and symmetric functions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0002.

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This chapter presents the study of a homogeneous stochastic higher spin six-vertex model in a quadrant. For this model concise integral representations for multipoint q-moments of the height function and for the q-correlation functions are derived. At least in the case of the step initial condition, these formulas degenerate in appropriate limits to many known formulas of such type for integrable probabilistic systems in the (1+1)d KPZ universality class, including the stochastic six-vertex model, ASEP, various q-TASEPs, and associated zero-range processes. The arguments are largely based on p

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42

DiBenedetto, Emmanuele, Ugo Gianazza, and Vincenzo Vespri. Harnack's Inequality for Degenerate and Singular Parabolic Equations. Springer New York, 2014.

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43

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

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44

Favini, Angelo, and Atsushi Yagi. Degenerate Differential Equations in Banach Spaces (Pure and Applied Mathematics) (Monographs and Textbooks in Pure and Applied Mathematics, 215). CRC, 1998.

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45

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

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46

Linear Sobolev Type Equations and Degenerate Semigroups of Operators. De Gruyter, Inc., 2003.

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47

Sviridyuk, Georgy A., and Vladimir E. Fedorov. Linear Sobolev Type Equations and Degenerate Semigroups of Operators. de Gruyter GmbH, Walter, 2012.

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48

Gazzola, Filippo, and Maurizio Garrione. Nonlinear Equations for Beams and Degenerate Plates with Piers. Springer, 2019.

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49

Zhan, Yi. Viscosity solutions of nonlinear degenerate parabolic equations and several applications. 2000.

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50

Horing, Norman J. Morgenstern. Graphene. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0012.

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Chapter 12 introduces Graphene, which is a two-dimensional “Dirac-like” material in the sense that its energy spectrum resembles that of a relativistic electron/positron (hole) described by the Dirac equation (having zero mass in this case). Its device-friendly properties of high electron mobility and excellent sensitivity as a sensor have attracted a huge world-wide research effort since its discovery about ten years ago. Here, the associated retarded Graphene Green’s function is treated and the dynamic, non-local dielectric function is discussed in the degenerate limit. The effects of a quan

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