2015/02/04 by H. Beirão da Veiga, da Veiga, Hugo Beirao
Mathematics · #26B30 #26B35 #35A09 #35B65 #35J25 #35Q30 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1502.01153
openalex publication_date 2015/02/04 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
About thirty years ago we looked for "minimal assumptions" on the data which\nguarantee that solutions to the ,2-D , evolution Euler equations in a\nbounded domain are classical. Classical means here that all the derivatives\nappearing in the equations and boundary conditions are continuous up to the\nboundary. Following a well known device, the above problem led us to consider\nthis same regularity problem for the Poisson equation under homogeneous\nDirichlet boundary conditions. At this point, one was naturally led to consider\nthe extension of this last problem to more general linear elliptic boundary\nvalue problems, and also to try to extend the results to more general data\nspaces. At that time, some side results in these directions remained\nunpublished. The first motivation for this note is a clear description of the\nroute followed by us in studying these kind of problems. New results and open\nproblems are also considered.\n