123 research outputs found
Global well-posedness for the 2 D quasi-geostrophic equation in a critical Besov space
We show that the the 2 D quasi-geostrophic equation has global and unique
strong solution, when the (large) data belongs in the critical, scale invariant
space \dot{B}^{2-2\al}_{2, \infty}\cap L^{2/(2\al-1)}
Optimal solvability for the Dirichlet and Neumann problem in dimension two
We show existence and uniqueness for the solutions of the regularity and the
Neumann problems for harmonic functions on Lipschitz domains with data in the
Hardy spaces H^p, p>2/3, where This in turn implies that solutions to the
Dirichlet problem with data in the Holder class C^{1/2}(\partial D) are
themselves in C^{1/2}(D). Both of these results are sharp. In fact, we prove a
more general statement regarding the H^p solvability for divergence form
elliptic equations with bounded measurable coefficients.
We also prove similar solvability result for the regularity and Dirichlet
problem for the biharmonic equation on Lipschitz domains
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