Sobolev regularity of the symmetric gradient of solutions to a class of $ϕ$-Laplacian systems
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| Format: | Preprint |
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2026
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| _version_ | 1866915838403018752 |
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| author | Giannetti, Flavia di Napoli, Antonia Passarelli |
| author_facet | Giannetti, Flavia di Napoli, Antonia Passarelli |
| contents | The paper deals with the second order regularity properties of the weak solutions $u\in W^{1,ϕ}(Ω, \real^n)$ } of systems of the form
\begin{equation*}\label{equareg}
-\dive A(x,\E u)=f,
\end{equation*}
in a bounded domain $Ω\subset\R^n$, $n>2$,
where the operator $ A(x,P)$ is Lipschitz continuous with respect to the $x$-variable and satisfies growth conditions with respect to the second variable expressed through a Young function $Φ$. We prove the Sobolev regularity of a function of the symmetric gradient $\E u$ that takes into account the nonlinear growth of the operator $A(x,P)$, {assuming that the force term $f$ belongs to a suitable Orlicz-Sobolev space. {The main result is achieved through some uniform higher differentiability estimates for solutions to a class of approximating problems, constructed adding singular higher order perturbations to the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05555 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sobolev regularity of the symmetric gradient of solutions to a class of $ϕ$-Laplacian systems Giannetti, Flavia di Napoli, Antonia Passarelli Analysis of PDEs 35J60, 35B65, 35Q35 The paper deals with the second order regularity properties of the weak solutions $u\in W^{1,ϕ}(Ω, \real^n)$ } of systems of the form \begin{equation*}\label{equareg} -\dive A(x,\E u)=f, \end{equation*} in a bounded domain $Ω\subset\R^n$, $n>2$, where the operator $ A(x,P)$ is Lipschitz continuous with respect to the $x$-variable and satisfies growth conditions with respect to the second variable expressed through a Young function $Φ$. We prove the Sobolev regularity of a function of the symmetric gradient $\E u$ that takes into account the nonlinear growth of the operator $A(x,P)$, {assuming that the force term $f$ belongs to a suitable Orlicz-Sobolev space. {The main result is achieved through some uniform higher differentiability estimates for solutions to a class of approximating problems, constructed adding singular higher order perturbations to the system. |
| title | Sobolev regularity of the symmetric gradient of solutions to a class of $ϕ$-Laplacian systems |
| topic | Analysis of PDEs 35J60, 35B65, 35Q35 |
| url | https://arxiv.org/abs/2603.05555 |