Existence of minimizers of multi-constrained variational problems for product functions

Abstract

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.

Keywords

• Multi-constrained
• variational
• elliptic systems
• non-compact