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 (15[1])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, (-5[1])who names the (*) boundary condition that constrains both a function and its derivative, which combines Dirichlet (“deer-ih-CLAY”) and Neumann conditions. This mathematician’s name is first in the pair of equations “du dx (10[1])equals dv dy” and “du dy equals negative dv dx,” which determine if a complex function is differentiable. For 10 points, what Frenchman co-names those equations with Riemann and (10[1])an inequality about inner products with Schwarz? ■END■ (10[1]0[1])

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