Quasilinear PDEs, Interpolation Spaces and Hölderian mappings

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 regul...

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Bibliographic Details
Published in:Analysis mathematica (Budapest) 2023-12, Vol.49 (4), p.895-950
Main Authors: Ahmed, I., Fiorenza, A., Formica, M. R., Gogatishvili, A., El Hamidi, A., Rakotoson, J. M.
Format: Article
Language:English
Subjects:
Analysis
Functionals
Interpolation
Mathematics
Mathematics and Statistics
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Summary: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 : T f = ∇ u is locally or globally α -Hölderian under suitable values of α and appropriate hypotheses on V and â .
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-023-0245-z