Explicit div-curl inequalities in bounded and unbounded domains of $${{\mathbb {R}}}^3$$ R 3
Résumé
We give a constructive proof of some functional inequalities related to the div and curl operators in bounded and unbounded domains of R3. Our new innovation consists in giving explicit constants in several geometric configurations. These inequalities are of a first use in solving div-curl systems and vector potential problems arising in physics.