Quasilinear PDEs, interpolation spaces and Hölderian mappings

0578437 - MÚ 2024 RIV HU eng J - Článek v odborném periodiku
Ahmed, I. - Fiorenza, A. - Formica, M. R. - Gogatishvili, Amiran - El Hamidi, A. - Rakotoson, J. M.
Quasilinear PDEs, interpolation spaces and Hölderian mappings.
Analysis Mathematica. Roč. 49, č. 4 (2023), s. 895-950. ISSN 0133-3852. E-ISSN 1588-273X
Grant CEP: GA ČR(CZ) GA23-04720S
Institucionální podpora: RVO:67985840
Klíčová slova: anisotropic-variable exponent * Hölderian operator * interpolation * quasilinear equation * regularity
Obor OECD: Pure mathematics
Impakt faktor: 0.7, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1007/s10476-023-0245-z

As in the work of Tartar [59], we develop here some new results on nonlinear interpolation of α-Hölderian mappings between normed spaces, by studying the action of the mappings on K-functionals and between interpolation spaces with logarithm functions. We apply these results to obtain some regularity results on the gradient of the solutions to quasilinear equations of the form − div (a^ (∇ u)) + V(u) = f, where V is a nonlinear potential and f belongs to non-standard spaces like Lorentz–Zygmund spaces. We show several results, for instance, that the mapping T:Tf=∇u is locally or globally α-Hölderian under suitable values of α and appropriate hypotheses on V and â.
Trvalý link: https://hdl.handle.net/11104/0347433