Direct Methods in the Calculus of Variations by Enrico Giusti

By Enrico Giusti

This booklet presents a finished dialogue at the life and regularity of minima of normal integrals within the calculus of diversifications and of recommendations to elliptic partial differential equations and platforms of the second one order. whereas direct equipment for the lifestyles of suggestions are popular and feature been regular within the final century, the regularity of the minima used to be constantly acquired through the Euler equation as part of the final concept of partial differential equations. during this booklet, utilizing the concept of the quasi-minimum brought via Giaquinta and the writer, the direct equipment are prolonged to the regularity of the minima of functionals within the calculus of adaptations, and of recommendations to partial differential equations. This unified remedy deals a considerable economic system within the assumptions, and allows a deeper realizing of the character of the regularity and singularities of the recommendations. The publication is largely self-contained, and calls for just a common wisdom of the weather of Lebesgue integration thought.

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