oups ▁of ▁transformations ▁on ▁Ban ach ▁spaces ▁and ▁the ▁theory ▁of ▁Hamilton – Jac obi ▁equations . ▁With ▁Pierre - Louis ▁L ions ▁he ▁did ▁research ▁on ▁the ▁vis cos ity ▁solutions ▁of ▁partial ▁differential ▁equations . ▁ ▁In ▁ 2 0 0 0 ▁he ▁was ▁elected ▁a ▁member ▁of ▁the ▁American ▁Academy ▁of ▁Arts ▁and ▁Sciences . ▁In ▁ 1 9 9 9 ▁he ▁received ▁the ▁L ero y ▁P . ▁Ste ele ▁Prize . ▁In ▁ 1 9 7 4 ▁he ▁was ▁an ▁Inv ited ▁L ect urer ▁( on ▁" Sem igr oups ▁of ▁non linear ▁equations ▁and ▁evolution ▁equations ") ▁at ▁the ▁International ▁Congress ▁of ▁Mathemat icians ▁in ▁V ancouver . ▁In ▁ 2 0 1 2 ▁he ▁became ▁a ▁fellow ▁of ▁the ▁American ▁Mathemat ical ▁Society . ▁ ▁Among ▁his ▁doctor al ▁students ▁are ▁Lawrence ▁C . ▁Evans ▁and ▁Pan agi ot is ▁E . ▁S oug an id is . ▁ ▁References ▁ ▁External ▁links ▁▁ ▁home ▁page ▁Cr and all ▁- ▁U C SB ▁Math . ▁De pt . ▁ ▁Ste ele ▁Prize ▁to ▁Cr and all , ▁pdf - file , ▁Notices ▁A MS ▁( 7 6   k B ) ▁ ▁Category : 1 9 4 0 ▁birth s ▁Category : L iving ▁people ▁Category : 2 0 th - century ▁American ▁mathemat icians ▁Category : 2 1 st - century ▁American ▁mathemat icians ▁Category : Math emat ical ▁anal yst s ▁Category : P DE ▁the or ists ▁Category : F ell ows