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A compact course on linear PDEs

Valli, Alberto.

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A compact course on linear PDEs

Record Type:	Electronic resources : Monograph/item
Title/Author:	A compact course on linear PDEs/ by Alberto Valli.
Author:	Valli, Alberto.
Published:	Cham :Springer International Publishing : : 2020.,
Description:	xiii, 235 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	1. Introduction -- 2. Second order linear elliptic equations -- 3. A bit of functional analysis -- 4. Weak derivatives and Sobolev spaces -- 5. Weak formulation of elliptic PDEs -- 6. Technical results -- 7. Additional results -- 8. Saddle points problems -- 9. Parabolic PDEs -- 10. Hyperbolic PDEs -- A Partition of unity -- B Lipschitz continuous and smooth domains -- C Integration by parts for smooth functions and vector ﬁelds -- D Reynolds transport theorem -- E Gronwall lemma -- F Necessary and suﬃcient conditions for the well-posedness of the variationalproblem.
Contained By:	Springer Nature eBook
Subject:	Differential equations, Partial. -
Online resource:	https://doi.org/10.1007/978-3-030-58205-0
ISBN:	9783030582050

A compact course on linear PDEs
Valli, Alberto.

A compact course on linear PDEs[electronic resource] /by Alberto Valli. - Cham :Springer International Publishing :2020. - xiii, 235 p. :ill. (some col.), digital ;24 cm. - Unitext: La matematica per il 3+2,v.1262038-5722 ;. - Unitext ;v.126..

1. Introduction -- 2. Second order linear elliptic equations -- 3. A bit of functional analysis -- 4. Weak derivatives and Sobolev spaces -- 5. Weak formulation of elliptic PDEs -- 6. Technical results -- 7. Additional results -- 8. Saddle points problems -- 9. Parabolic PDEs -- 10. Hyperbolic PDEs -- A Partition of unity -- B Lipschitz continuous and smooth domains -- C Integration by parts for smooth functions and vector ﬁelds -- D Reynolds transport theorem -- E Gronwall lemma -- F Necessary and suﬃcient conditions for the well-posedness of the variationalproblem.

This textbook is devoted to second order linear partial differential equations. The focus is on variational formulations in Hilbert spaces. It contains elliptic equations, including some basic results on Fredholm alternative and spectral theory, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their properties, saddle point problems, parabolic equations and hyperbolic equations. Many exercises are added, and the complete solution of all of them is included. The work is mainly addressed to students in Mathematics, but also students in Engineering with a good mathematical background should be able to follow the theory presented here.

ISBN: 9783030582050

Standard No.: 10.1007/978-3-030-58205-0doiSubjects--Topical Terms:

518115
Differential equations, Partial.

LC Class. No.: QA320 / .V35 2020

Dewey Class. No.: 515.353

A compact course on linear PDEs
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100 1 $a Valli, Alberto. $3 1245745
245 1 2 $a A compact course on linear PDEs $h [electronic resource] / $c by Alberto Valli.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a xiii, 235 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Unitext: La matematica per il 3+2, $x 2038-5722 ; $v v.126
505 0 $a 1. Introduction -- 2. Second order linear elliptic equations -- 3. A bit of functional analysis -- 4. Weak derivatives and Sobolev spaces -- 5. Weak formulation of elliptic PDEs -- 6. Technical results -- 7. Additional results -- 8. Saddle points problems -- 9. Parabolic PDEs -- 10. Hyperbolic PDEs -- A Partition of unity -- B Lipschitz continuous and smooth domains -- C Integration by parts for smooth functions and vector ﬁelds -- D Reynolds transport theorem -- E Gronwall lemma -- F Necessary and suﬃcient conditions for the well-posedness of the variationalproblem.
520 $a This textbook is devoted to second order linear partial differential equations. The focus is on variational formulations in Hilbert spaces. It contains elliptic equations, including some basic results on Fredholm alternative and spectral theory, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their properties, saddle point problems, parabolic equations and hyperbolic equations. Many exercises are added, and the complete solution of all of them is included. The work is mainly addressed to students in Mathematics, but also students in Engineering with a good mathematical background should be able to follow the theory presented here.
650 0 $a Differential equations, Partial. $3 518115
650 0 $a Functional analysis. $3 531838
650 1 4 $a Partial Differential Equations. $3 890899
650 2 4 $a Computational Mathematics and Numerical Analysis. $3 891040
650 2 4 $a Functional Analysis. $3 893943
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773 0 $t Springer Nature eBook
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950 $a Mathematics and Statistics (SpringerNature-11649)