Direct Methods in the Calculus of Variations (BOK)

Enrico Giusti

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A comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. While direct methods for the existence of solutions are well-known and were widely-used in the 20th century, the regularity of the minima was always obtained by means of the Euler equation as a part of the general theory of partial differential equations. In this work, using the notion of the quasi-minimum introduced by Giaquinta and the author, the direct methods are extended to the regularity of the minima of functionals in the calculus of variations, and of solutions to partial differential equations. This unified treatment offers a substantial economy in the assumptions, and permits a deeper understanding of the nature of the regularity and singularities of the solutions. The volume is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory.


Språk Engelsk Engelsk Forfatter Enrico Giusti
World Scientific Publishing UK
ISBN 9789812380432
Antall sider 370 Dimensjoner 16cm x 23cm x 2,5cm
Vekt 717 gram Leverandør Bertram Trading Ltd
Emner og form Calculus of variations