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Let Omega be a bounded, simply connected domain with boundary of classC^{1,1} except at finitely many points S_j where the boundary is locally acorner of aperture alpha_j<=pi/2. Improving on results of Grisvard, we showthat the solution Gf to the Dirichlet problem on Omega with data f inL^infinity(Omega) and homogeneous boundary conditions has exponentiallyintegrable second derivatives. The proof uses sharp L^p bounds for singularintegrals on power weighted spaces inspired by the work of Buckley. Our resultsallow for the extension of the Yudovich theory of existence, uniqueness andregularity of weak solutions to the Euler equations on Omega x (0,T) topolygonal domains Omega as above.

Grisvard's shift theorem near L^infinity and Yudovich theory on polygonal domains