Sobolev Spaces and Elliptic Partial Differential Equations: Variational Method using Lax-Milgram Theorem - Couverture souple

Iyiola, Olaniyi

 
9783659142000: Sobolev Spaces and Elliptic Partial Differential Equations: Variational Method using Lax-Milgram Theorem
Couverture souple
ISBN 10 : 365914200X ISBN 13 : 9783659142000
Editeur : LAP LAMBERT Academic Publishing, 2012

Synopsis

The main objective to the study of theory of Partial Differential Equations (PDEs) is to insure or find out properties of solutions of PDE that are not directly attainable by direct analytical means. Certain function spaces have certain known properties for which solutions of PDEs can be classified. As a result, this work critically looked into some function spaces and their properties. We consider extensively, Lp-spaces, distribution theory and sobolev spaces. The emphasis is made on sobolev spaces, which permit a modern approach to the study of differential equations. Looking at the linear elliptic partial differential equations considered in this work, we see that the key is Lax-Milgram theorem and the full understanding of Sobolev spaces and its properties. We are able to remove the rigor associated with second order partial differential equations and present it in the form that we can easily handle through the function spaces discussed. The book is based on variational formulation of some Boundary Value Problems (PDEs) using some known theorem (Lax-Milgram Theorem) to ascertain the existence and uniqueness of weak solution to such linear Elliptic PDEs.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

The main objective to the study of theory of Partial Differential Equations (PDEs) is to insure or find out properties of solutions of PDE that are not directly attainable by direct analytical means. Certain function spaces have certain known properties for which solutions of PDEs can be classified. As a result, this work critically looked into some function spaces and their properties. We consider extensively, Lp-spaces, distribution theory and sobolev spaces. The emphasis is made on sobolev spaces, which permit a modern approach to the study of differential equations. Looking at the linear elliptic partial differential equations considered in this work, we see that the key is Lax-Milgram theorem and the full understanding of Sobolev spaces and its properties. We are able to remove the rigor associated with second order partial differential equations and present it in the form that we can easily handle through the function spaces discussed. The book is based on variational formulation of some Boundary Value Problems (PDEs) using some known theorem (Lax-Milgram Theorem) to ascertain the existence and uniqueness of weak solution to such linear Elliptic PDEs.

Biographie de l'auteur

Mr Iyiola Olaniyi S., a lecturer at Nigerian Turkish Nile University, got his B.Sc.Degree Cert.from University of Nigeria and his M.Sc.Degree Cert. from African University of Science and Tech.,AUST-Nigeria and a PhD student of Obafemi Awolowo University,Nigeria all in Mathematics. He is currently been awarded a Research (Innovation) Fellow at AUST.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2012
Langue
anglais
ISBN 10 
365914200X
ISBN 13 
9783659142000
Reliure
Broché
Nombre de pages
108
Coordonnées du fabricant
non disponible
Personne responsable
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