2013/01/08 by A. C. L. Ashton, A. S. Fokas, Ashton, A. C. L. +1 · 5 citations
Computer Science · Engineering · Mathematics · #35B65 #35D30 #35J25 #Analysis of PDEs (math.AP) #Boundary (topology) #Boundary value problem #Composite Material Mechanics #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Geometry #Mathematical analysis #Mathematical optimization #Mathematics #Numerical methods in engineering #Regular polygon #Statistics #Value (mathematics) #math.AP #msc:35B65 #msc:35D30 #msc:35J25
paper · pdf · doi:10.48550/arxiv.1301.1490
published in arXiv (Cornell University) (Cornell University) · 25 pages, 4 figures
arxiv created 2013/01/08 · openalex publication_date 2013/01/08 · arxiv updated 2013/01/09 · openalex created_date 2017/01/06 · openalex updated_date 2026/07/28
We use novel integral representations developed by the second author to prove certain rigorous results concerning elliptic boundary value problems in convex polygons. Central to this approach is the so-called global relation, which is a non-local equation in the Fourier space that relates the known boundary data to the unknown boundary values. Assuming that the global relation is satisfied in the weakest possible sense, i.e. in a distributional sense, we prove there exist solutions to Dirichlet, Neumann and Robin boundary value problems with distributional boundary data. We also show that the analysis of the global relation characterises in a straightforward manner the possible existence of both integrable and non-integrable corner-singularities.