2008/10/19 by Burak Aksoylu, Aksoylu, Burak, Horst R. Beyer +1
Computer Science · Engineering · Mathematics · #35J25 #47F05 #65J10 #65N99 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.FA #msc:35J25 #msc:47F05 #msc:65J10 #msc:65N99
paper · pdf · doi:10.48550/arxiv.0810.3427
arxiv created 2008/10/19 · openalex publication_date 2008/10/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the behaviour of the solutions of the stationary diffusion equation as a function of a possibly rough (L∞-) diffusivity. This includes the boundary behaviour of the solution maps, associating to each diffusivity the solution corresponding to some fixed source function, when the diffusivity approaches infinite values in parts of the medium. In n-dimensions, n ≥ 1, by assuming a weak notion of convergence on the set of diffusivities, we prove the strong sequential continuity of the solution maps. In 1-dimension, we prove a stronger result, i.e., the unique extendability of the map of solution operators, associating to each diffusivity the corresponding solution operator, to a sequentially continuous map in the operator norm on a set containing `diffusivities' assuming infinite values in parts of the medium. In this case, we also give explicit estimates on the convergence behaviour of the map.