Packet 4: Tossup 5

This mathematician’s name appears first in a theorem whose analyticity assumption cannot be relaxed to smoothness, by Lewy’s example. Sofya (15[1])Kovalevskaya generalized this mathematician’s result about local existence and uniqueness of PDE (-5[2])solutions. (-5[2])Problems named for this mathematician (15[1]-5[1])can be solved (-5[2])via Picard iteration to a fixed point. (-5[1])Initial value problems are often named for this mathematician, (-5[1])who names the (15[1])(*) boundary (-5[1])condition (-5[1])that constrains both a function (-5[1])and its derivative, (-5[2])which combines (-5[1])Dirichlet (“deer-ih-CLAY”) and Neumann conditions. (0[1])This (10[1])mathematician’s (-5[1])name (-5[2])is first in the pair of equations “du dx (10[1])equals (10[1])dv dy” (10[1])and “du (10[1])dy equals negative dv (10[1])dx,” which determine if a (10[1])complex function is differentiable. (10[2]-5[1])For 10 points, what Frenchman (10[1])co-names (10[1])those equations with Riemann (10[2])and (10[1])an inequality about inner products (10[2])with (10[1])Schwarz? (10[3])■END■ (10[12]0[2])

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