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Fractional differentiability for solutions of the inhomogeneous p-Laplace system

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cris.lastimport.scopus2024-02-12T20:44:55Z
dc.abstract.enIt is shown that if $p \ge 3$ and $u \in W^{1,p}(\Omega,\mathbb{R}^N)$ solves the inhomogenous $p$-Laplace system \[ \operatorname{div} (|\nabla u|^{p-2} \nabla u) = f, \qquad f \in W^{1,p'}(\Omega,\mathbb{R}^N), \] then locally the gradient $\nabla u$ lies in the fractional Nikol'ski{\u\i} space $\mathcal{N}^{\theta,2/\theta}$ with any $\theta \in [ \tfrac{2}{p}, \tfrac{2}{p-1} )$. To the author's knowledge, this result is new even in the case of $p$-harmonic functions, slightly improving known $\mathcal{N}^{2/p,p}$ estimates. The method used here is an extension of the one used by A. Cellina in the case $2 \le p < 3$ to show $W^{1,2}$ regularity.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorMiśkiewicz, Michał
dc.date.accessioned2024-01-25T01:15:35Z
dc.date.available2024-01-25T01:15:35Z
dc.date.issued2018
dc.description.financeNie dotyczy
dc.description.volume146
dc.identifier.doi10.1090/PROC/13993
dc.identifier.issn0002-9939
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/107446
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofProceedings of the American Mathematical Society
dc.relation.pages3009-3017
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.subject.enp-Laplacian degenerate elliptic systems fractional order Nikol’ski spaces
dc.titleFractional differentiability for solutions of the inhomogeneous p-Laplace system
dc.typeJournalArticle
dspace.entity.typePublication