As in the work of Tartar [59], we develop here some new results on nonlinear interpolation of α-H¨olderian 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 : T f = ∇u is locally or globally α-H¨olderian under suitable values of α and appropriate hypotheses on V and a.
Quasilinear PDEs, Interpolation Spaces and Hölderian mappings / Ahmed, I.; Fiorenza, A.; Formica, M. R.; Gogatishvili, A.; El Hamidi, A.; Rakotoson, J. M.. - In: ANALYSIS MATHEMATICA. - ISSN 0133-3852. - 49:4(2023), pp. 895-950. [10.1007/s10476-023-0245-z]
Quasilinear PDEs, Interpolation Spaces and Hölderian mappings
Fiorenza, A.;
2023
Abstract
As in the work of Tartar [59], we develop here some new results on nonlinear interpolation of α-H¨olderian 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 : T f = ∇u is locally or globally α-H¨olderian under suitable values of α and appropriate hypotheses on V and a.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
