Concepedia

Remarks on the paper: “Basic calculus of variations”

Pacific Journal of Mathematics · 1985 · 47 citations · 17 references

Open access

Concepts

Natural SciencesIndustrial EngineeringStochastic ProcessesCalculus Of VariationsIntegral EquationsMultiple IntegralsLower SemicontinuitySetting Up Multiple Integrals

Abstract

We show that a condition studied in E. Silverman's paper is not, as claimed, necessary for lower semicontinuity of multiple integrals in the calculus of variations.

References

17

Convexity conditions and existence theorems in nonlinear elasticity

J. M. Ball · Archive for Rational Mechanics and Analysis · 1976 · 2.4K citations

Engineering, Mechanical Engineering, Applied Mechanics +15

Quasi-convexity and the lower semicontinuity of multiple integrals

Charles B. Morrey · Pacific Journal of Mathematics · 1952 · 688 citations · Full text

Natural Sciences, High-performance Computing, Interior Construction +10

Null Lagrangians, weak continuity, and variational problems of arbitrary order

J. M. Ball, J. C. Currie, Peter J. Olver · Journal of Functional Analysis · 1981 · 327 citations

Natural Sciences, Mathematics, Mechanical Engineering +16

Unconditional bases and fixed points of nonexpansive mappings

Pei-Kee Lin · Pacific Journal of Mathematics · 1985 · 96 citations · Full text

Social Sciences, Property Law, Contract Theory +10

On the atomic decomposition for Hardy spaces

James Wilson · Pacific Journal of Mathematics · 1985 · 70 citations · Full text

Natural Sciences, Physics, Representation Theory +7