ère ▁equation ▁and ▁a ▁partial ▁regular ity ▁result ▁for ▁Mon ge – A mp ère ▁type ▁equations , ▁both ▁proved ▁together ▁with ▁Gu ido ▁de ▁Philipp is . ▁He ▁used ▁optimal ▁transport ▁techniques ▁to ▁get ▁improved ▁versions ▁of ▁the ▁an is otrop ic ▁is oper imet ric ▁inequality , ▁and ▁obtained ▁several ▁other ▁important ▁results ▁on ▁the ▁stability ▁of ▁functional ▁and ▁geometric ▁in equal ities . ▁In ▁particular , ▁together ▁with ▁Francesco ▁Mag gi ▁and ▁Ald o ▁Pr at elli , ▁he ▁proved ▁a ▁sharp ▁quant itative ▁version ▁of ▁the ▁an is otrop ic ▁is oper imet ric ▁inequality . ▁ ▁Then , ▁in ▁a ▁joint ▁work ▁with ▁Eric ▁Car len , ▁he ▁addressed ▁the ▁stability ▁analysis ▁of ▁some ▁G agli ardo – N ir enberg ▁and ▁log arith mic ▁Hard y – L ittle wood – S ob ole v ▁in equal ities ▁to ▁obtain ▁a ▁quant itative ▁rate ▁of ▁convergence ▁for ▁the ▁critical ▁mass ▁K eller – Seg el ▁equation . ▁He ▁also ▁worked ▁on ▁Hamilton – Jac obi ▁equations ▁and ▁their ▁connections ▁to ▁weak ▁Kol m og or ov – Ar n old – M oser ▁theory . ▁In ▁a ▁paper ▁with ▁Gonz alo ▁Con tr eras ▁and ▁Lud ov ic ▁R iff ord , ▁he ▁proved ▁generic ▁hyper bol icity ▁of ▁A ub ry ▁sets ▁on ▁compact ▁surfaces . ▁ ▁In ▁addition , ▁he ▁has ▁given ▁several ▁contributions ▁to ▁the ▁Di ▁P erna – L ions ' ▁theory , ▁applying ▁it ▁both ▁to ▁the ▁understanding ▁of ▁sem ic lass