Abstract
We discuss new local regularity estimates related to the p-Poisson equation −div(A(∇u)) = −divF for p > 2. In the planar case d = 2 we are able to transfer local interior Besov and Triebel-Lizorkin regularity up to first order derivatives from the forcing term F to the flux \(A(\nabla u)=\left | \nabla u \right |{ }^{p-2}\nabla u\). In case of higher dimensions or systems we have a smallness restriction on the corresponding smoothness parameter. Apart from that, our results hold for all reasonable parameter constellations related to weak solutions u ∈ W 1, p( Ω) including quasi-Banach cases with applications to adaptive finite element analysis.
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Acknowledgements
The research of Anna Kh. Balci was partly supported by Russian Foundation for Basic Research project 19-01-00184 in Vladimir State University named after Alexander and Nikolay Stoletovs and by the German Research Foundation (DFG) through the CRC 1283.
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Kh. Balci, A., Diening, L., Weimar, M. (2021). Higher Order Regularity Shifts for the p-Poisson Problem. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_114
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