Singular Solutions of Nonlinear Elliptic and Parabolic Equations
Seiten
2016
De Gruyter (Verlag)
978-3-11-031548-6 (ISBN)
De Gruyter (Verlag)
978-3-11-031548-6 (ISBN)
The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Please submit book proposals to Jürgen Appell.
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
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
Alexander A. Kovalevsky, Igor I. Skrypnik, and Andrey E. Shishkov, National Academy of Sciences of Ukraine,Donetsk, Ukraine.
| Erscheint lt. Verlag | 21.3.2016 |
|---|---|
| Reihe/Serie | De Gruyter Series in Nonlinear Analysis and Applications ; 24 |
| Verlagsort | Berlin/Boston |
| Sprache | englisch |
| Maße | 170 x 240 mm |
| Gewicht | 881 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | Analysis • -data • Differential Equations • Differential equations, Elliptic • Differential equations, Nonlinear • Differential equations, Parabolic • Differentialgleichung • Dirichlet problem • Elliptic • Entscheidungen • Équations différentielles elliptiques • Équations différentielles non linéaires • Équations différentielles paraboliques • Existence • Isolated singularities • Landesverfassungsgerichte • Localized boundary blow-up regimes • Lösung • Mathematics • Mathematik • Nichtlineare Analysis • Nichtlineare elliptische Differentialgleichung • Nichtlineare parabolische Differentialgleichung • Nonlinear • Nonlinear elliptic equations of the second and fou • Nonlinear elliptic equations of the second and fourth order • Nonlinear elliptic equations of the second and fourth order, -data, Dirichlet problem, existence, u • Nonlinear elliptic equations of the second and fourth order, -data, Dirichlet problem, existence, u • Nonlinear elliptic equations of the second and fourth order, -data, Dirichlet problem, existence, un • Nonlinear elliptic equations of the second and fourth order, -data, Dirichlet problem, existence, uniqueness and summability of solutions, Quasilinear parabolic equations of the second and high order, • Nonlinear elliptic equations of the second and fourth order, -data, Dirichlet problem, existence, uniqueness and summability of solutions, Quasilinear parabolic equations of the second and high order, Isolated singularities, removability of singularities, • Nonlinear elliptic equations of the second and fourth order, -data, Dirichlet problem, existence, uniqueness and summability of solutions, Quasilinear parabolic equations of the second and high order, Isolated singularities, removability of singularities • Nonlinear elliptic equations of the second and fourth order, -data, Dirichlet problem, existence, uniqueness and summability of solutions, Quasilinear parabolic equations of the second and high order, Isolated singularities, removability of singularities, Localized boundary blow-up regimes, nonlocalized boundary regimes with peaking. • nonlocalized boundary regimes with peaking. • parabolic • Quasilinear parabolic equations of the second and high order • removability o • removability of singularities • Singuläre Lösung • uniqueness and summability of solutions |
| ISBN-10 | 3-11-031548-3 / 3110315483 |
| ISBN-13 | 978-3-11-031548-6 / 9783110315486 |
| Zustand | Neuware |
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