Round 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 Kovalevskaya generalized this mathematician’s result about local existence and uniqueness of PDE solutions. Problems named for this mathematician can be solved via Picard iteration to a fixed point. Initial value problems are often named for this mathematician, who names the (*) boundary condition that constrains both a function and its derivative, (-5[1])which combines Dirichlet (“deer-ih-CLAY”) and Neumann conditions. This (10[1])mathematician’s name is first in the pair of equations “du dx equals dv dy” and “du (10[1])dy equals negative dv dx,” which determine if a (10[1])complex function is differentiable. For 10 points, what Frenchman co-names (10[1])those equations with Riemann and an inequality about inner products (10[1])with Schwarz? ■END■ (10[1])

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