Applications of Interpolation theory to the regularity of some quasilinear PDEs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00619397" target="_blank" >RIV/67985840:_____/25:00619397 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.15673/pigc.v18i1.2865" target="_blank" >https://doi.org/10.15673/pigc.v18i1.2865</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.15673/pigc.v18i1.2865" target="_blank" >10.15673/pigc.v18i1.2865</a>

Result language
angličtina
Original language name
Applications of Interpolation theory to the regularity of some quasilinear PDEs
Original language description
We present some regularity results on the gradient of the weak or entropic-renormalized solution $u$ to the homogeneous Dirichlet problem for the quasilinear equations of the formnbegin{equation*}label{p-laplacian_eq} -div(|abla u|^{p-2} abla u)+V(x,u)=f, end{equation*} where $Omega$ is a bounded smooth domain of $mathbb R^n$, $V$ is a nonlinear potential and $f$ belongs to non-standard spaces like Lorentz-Zygmund spaces. nThe results, which have been exposed by the third author in a talk presented in AGMA 2024, the International Scientific Online Conference «Algebraic and geometric methods of analysis», May 27-30, 2024, Ukraine, constitute only a part of results proved in detail in a paper coauthored with I. Ahmed, A. Fiorenza, A. Gogatishvili, A. El Hamidi and J.M. Rakotoson.nMoreover, we collect some well-known and new results of the identication of some interpolation spaces and we enrich some contents with details.
Czech name
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Czech description
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Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS 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
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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