Abstract
Existence is established of a piecewise-convex, periodic, planar curve S below which is defined a harmonic function which simultaneously satisfies prescribed Dirichlet and Neumann boundary conditions on S. In hydrodynamics this corresponds to the existence of a periodic Stokes wave of extreme form which has a convex profile between consecutive stagnation points where there is a corner with a contained angle of 120°
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Plotnikov, P., Toland, J. Convexity of Stokes Waves of Extreme Form. Arch. Rational Mech. Anal. 171, 349–416 (2004). https://doi.org/10.1007/s00205-003-0292-3
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DOI: https://doi.org/10.1007/s00205-003-0292-3