On the calculus of variations in two variables
โ Scribed by Lamberto Cesari
- Publisher
- John Wiley and Sons
- Year
- 1956
- Tongue
- English
- Weight
- 523 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0010-3640
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๐ SIMILAR VOLUMES
We prove necessary optimality conditions for problems of the calculus of variations on time scales with a Lagrangian depending on the free end-point.
In this paper we prove the two-dimensional pointwise dyadic differentiability (provided that the distance of the indices is bounded) of the dyadic integral of integrable two-dimensional functions. We also prove some inequality of type (H, L 1 ) for the maximal operator sup n # N 2 |d n (If )|.
The purpose of this paper is to calculate the first variation of capacity and of the lowest eigenvalue for the Dirichlet problem in convex domains in R N . These formulas are well known in the smooth case and are due to Poincare and Hadamard, respectively. The point is to prove them in sufficient ge