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Titlebook: Nonlinear Partial Differential Equations for Future Applications; Sendai, Japan, July Shigeaki Koike,Hideo Kozono,Shigeru Sakaguchi Confer

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High-Energy Eigenfunctions of the Laplacian on the Torus and the Sphere with Nodal Sets of Complicaned in a contractible subset of .. We show that for any sufficiently large enough odd integer . there exists an eigenfunctions . of the Laplacian on . or . satisfying . (with . or . on . or ., respectively), and with a connected component of the nodal set of . given by ., up to an ambient diffeomorp
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Uniform Regularity for a Compressible Gross-Pitaevskii-Navier-Stokes System,Uniform regularity estimates are proved for a compressible Gross-Pitaevskii-Navier-Stokes system in . with ..
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,Regularity of Solutions of Obstacle Problems –Old & New–,Two kinds of machinery to show regularity of solutions of bilateral/unilateral obstacle problems are presented. Some generalizations of known results in the lit- erature are included. Several important open problems in the topics are given.
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