Hochschulschrift
Maximal Lp-Lq regularity for discrete elliptic differential operators
Maximal regularity estimates play an important role in the analysis of parabolic problems. In particular, maximal regularity estimates are very useful for nonlinear parabolic problems. Therefore, in this book, maximal regularity estimates for approximations of solutions of parabolic differential equations by finite elements or finite differences are investigated. In this context, one has to show that maximal regularity estimates are independent of the mesh. More precisely, uniform estimates for a family of finite element (finite difference) operators are shown. These estimates are used to prove uniqueness and existence of a local, strong solution for approximations of semilinear problems. Moreover, uniform maximal regularity estimates lead to a new approach for proving error estimates. Finally, error estimates in the linear and semilinear case are proved.
- Location
-
Deutsche Nationalbibliothek Frankfurt am Main
- ISBN
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9783936846515
3936846510
- Dimensions
-
24 cm
- Extent
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XI, 127 S.
- Language
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Englisch
- Notes
-
graph. Darst.
Zugl.: Darmstadt, Techn. Univ., Diss., 2003
- Classification
-
Mathematik
- Keyword
-
Parabolische Differentialgleichung
Finite-Elemente-Methode
Finite-Differenzen-Methode
Elliptischer Differentialoperator
Regularität
- Event
-
Veröffentlichung
- (where)
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Berlin
- (who)
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wvb, Wiss. Verl. Berlin
- (when)
-
2003
- Creator
-
Geißert, Matthias
- Table of contents
- Rights
-
Bei diesem Objekt liegt nur das Inhaltsverzeichnis digital vor. Der Zugriff darauf ist unbeschränkt möglich.
- Last update
- 11.06.2025, 2:24 PM CEST
Data provider
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Object type
- Hochschulschrift
Associated
- Geißert, Matthias
- wvb, Wiss. Verl. Berlin
Time of origin
- 2003
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Maximal Lp-Regularity of Parabolic Problems with Boundary Dynamics of Relaxation Type
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Maximal $$L^q$$ L q -Regularity for Parabolic Hamilton–Jacobi Equations and Applications to Mean Field Games
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Inhomogeneous symbols, the Newton polygon, and maximal Lp-regularity
Maximal regularity for elliptic operators with second-order discontinuous coefficients
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