Wu and Whitney 
l 
2 2 
[ be 9) F2E pee Re * eet trey J dé > 0...) Gey 
By substituting (14) in (24a), interchanging the order of integration 
according to the Poincaré-Bertrand formula (Muskhelishvili, 1953) 
wherever applicable, it can be shown that (24a) can also be written 
as 
(24b) 
1 1 
| Foe ry, ae ‘: AOE) s(t) or(eyat 
E: B 
aaa -1 -1 
di > 0 
where 
g(é) = a aay soe vats CER)? eae Fig + HLF, I 
If we suppose that F s+ eee Pees are Holder continuous, and 
consider a special choice of 2 6T which vanishes for |e - EG | 76 9 tg 
bounded (orl B) and is of one sign for |é ~ Es <€, where §& ° 
is any interior point of (-1,1), then it can be shown that the first 
term on the left side of (24b) predominates, hence a necessary con- 
dition for (24 b) to hold true is the inequality g(&) > 0, or 
E espa Fag >0 ( || ra Yoo (24c) 
This condition is analogous to the Legendre condition in the classical 
theory. 
The preceding illustrates the method of solution of the ex- 
tremum problem by singular integral equations. We should reiterate 
that the integral equations are nonlinear unless F is quadratic in I 
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