Quasilinear PDEs, interpolation spaces and Hölderian mappings

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00578437" target="_blank" >RIV/67985840:_____/23:00578437 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10476-023-0245-z" target="_blank" >https://doi.org/10.1007/s10476-023-0245-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10476-023-0245-z" target="_blank" >10.1007/s10476-023-0245-z</a>

Result language
angličtina
Original language name
Quasilinear PDEs, interpolation spaces and Hölderian mappings
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA23-04720S" target="_blank" >GA23-04720S: Fine properties of functions, operators and function spaces</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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