Функциональный анализ
Functional analysis: Philippe Ciarlet established weak forms of Poincaré's lemma and conditions of compatibility of Saint Venant, in Sobolev's spaces with negative exponents; he established that there are deep relationships between Jacques-Louis Lions' lemma, Nečas's inequality, Rham's theorem, and Bogovskii's theorem, which provide new methods to establish these results.