Existence of minimizers of multi-constrained variational problems for product functions
Huda Al Saud, Hichem Hajaiej · DOAJ (DOAJ: Directory of Open Access Journals) · 2018
We prove the existence of minimizers of a class of multi-constrained variational problems in which the non linearity involved is a product function not satisfying compactness, monotonicity, neither symmetry properties. Our result cannot be covered by previous studies that considered only a particular class of integrands. A key step is establishing the strict sub-additivity condition in the vectorial setting. This inequality is also interesting in itself.