Abstract
This paper deals with some functional-analytic questions which arise when the Stokes-wave problem, for the free boundary of a steady irrotational water wave, is formulated as a quadratic equation for a 2 π -periodic, real-valued function w on R which need not be weakly differentiable. It is shown how any solution w of bounded variation which lies in the fractional order Sobolev space H 1/2 must be real-analytic and describes the profile of a steady water wave. The investigation involves only elementary real and complex Hardy space theory.
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