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Analytic regularity for the Navier-Stokes equations in polygons with mixed boundary conditions
(2021)SAM Research ReportWe prove weighted analytic regularity of Leray-Hopf variational solutions for the stationary, incompressible Navier-Stokes Equations (NSE) in plane polygonal domains, subject to analytic body forces. We admit mixed boundary conditions which may change type at each vertex, under the assumption that homogeneous Dirichlet (''no-slip'') boundary conditions are prescribed on at least one side at each vertex of the domain. The weighted analytic ...Report -
Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations
(2021)SAM Research ReportReport -
Weighted analytic regularity for the integral fractional Laplacian in polygons
(2021)SAM Research ReportWe prove weighted analytic regularity of solutions to the Dirichlet problem for the integral fractional Laplacian in polygons with analytic right-hand side. We localize the problem through the Caffarelli-Silvestre extension and study the tangential differentiability of the extended solutions, followed by bootstrapping based on Caccioppoli inequalities on dyadic decompositions of vertex, edge, and edge-vertex neighborhoods.Report