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arXiv · 2502.08627

Calder\'on-Zygmund estimates for higher order elliptic equations in Orlicz-Sobolev spaces

Julián Fernández Bonder·Pablo Ochoa·Analía Silva
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Abstract

In this paper we obtain Calder\'on-Zygmund estimates for the laplacian of the following fourth order quasilinear elliptic problem $$ \Delta(g(\Delta u)\Delta u) = \Delta(g(\Delta f)\Delta f). $$ where the primitive of $g(t)t$, $G(t)$, is an $N-$function. We prove that if $G(f)\in L^q$, then $G(\Delta u)\in L^q$ for $q\ge 1$.

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Julián Fernández Bonder, Pablo Ochoa, Analía Silva. 2025-02-12. Calder\'on-Zygmund estimates for higher order elliptic equations in Orlicz-Sobolev spaces. https://arxiv.org/abs/2502.08627

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