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.
Quasilinear PDEs, Interpolation Spaces and Hölderian mappings
Formica M. R.;
2023-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
