Singular solutions of nonlinear elliptic and parabolic equations /

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This monograph looks at several trends of investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions to these equations. It will be useful for researchers and post-graduate students that specia...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Kovalevsky, Alexander A.
Otros Autores: Skrypnik, I. V., Shishkov, Andrey E.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin ; Boston : De Gruyter, [2016]
Colección:De Gruyter series in nonlinear analysis and applications ; 24.
Temas:
Differential equations, Elliptic.
Differential equations, Nonlinear.
Differential equations, Parabolic.
Équations différentielles elliptiques.
Équations différentielles non linéaires.
Équations différentielles paraboliques.
MATHEMATICS > Calculus.
MATHEMATICS > Mathematical Analysis.
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.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Foreword ; I. Nonlinear elliptic equations with L1-data ; 1. Nonlinear elliptic equations of the second order with L1-data ; 1.1 Introduction ; 1.2 General conditions for the limiting summability of solutions.
  • 1.3 The cases where the right-hand side of the equation belongs to logarithmic classes 1.4 On the integrally logarithmic conditions for the limiting summability of solutions ; 1.5 The case where the right-hand side of equation belongs to Lebesgue spaces close to L1(O).
  • 1.6 On the convergence of functions from satisfying special integral inequalities 1.7 On the existence of entropy solutions for the equations with degenerate coercivity and L1-data ; 1.8 A priori properties of the entropy solutions of equations with degenerate coercivity and L1-data.
  • 2. Nonlinear equations of the fourth order with strengthened coercivity and L1-data 2.1 Introduction ; 2.2 Set of functions ; 2.3 Definition and some properties of entropy solutions ; 2.4 One a priori estimate for the entropy solutions ; 2.5 Notion of H-solution.
  • 2.6 On uniqueness of the entropy solution 2.7 Theorems on existence ; 2.8 Entropy solutions as elements of the Sobolev spaces and the existence of W-solutions ; 2.9 On the summability of functions from satisfying certain integral inequalities.

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