2018/10/31 by Ricardo Weder, Albeverio, Sergio, Balslev, Anindita
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Boundary (topology) #Boundary value problem #Bounded function #Computer science #Dirichlet distribution #Hilbert space #Lebesgue integration #Mathematical analysis #Mathematics #Numerical methods in inverse problems #Pure mathematics #Sobolev space #Space (punctuation) #Spectral Theory in Mathematical Physics #Spectral theory #Standard probability space #TRACE (psycholinguistics) #math.AP #msc:35F35 #msc:35G15 #msc:35P10 #msc:35P25
paper · pdf · doi:10.1007/978-3-030-68490-7
published as in, Schrödinger Operators, Spectral Analysis and Number Theory in Memory of Erik Balslev, pp 271-294. Editors S. Albeverio, A. Balslev, and R. Weder. Springer Proceedings in Mathematics & Statistics, vol 348, Sringer, Switzerland, 2021 · I have changed the title, I have corrected missprints, I slightly edited the manuscript and I added publication details
openalex publication_date 2021/01/01 · arxiv created 2021/08/06 · arxiv updated 2021/08/09 · openalex created_date 2022/02/24 · openalex updated_date 2026/08/05
We study bounded trace maps on hypersurfaces for Sobolev spaces from a point of view that is fundamentally different from the one in the classical theory. This allows us to construct bounded trace maps under weak regularity assumptions on the hypersurfaces. In the case of bounded domains in \mathbf Rn we only require the continuity of the boundary. For hypersurfaces in the whole space \mathbf Rn we only assume that the hypersurfaces are Lebesgue measurable. As an application of our trace maps we consider the Dirichlet problem and we prove a coarea formula where the level sets are only assumed to be Lebesgue measurable hypersurfaces.