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arXiv · 2502.17067

Global second order optimal regularity for the vectorial $p$-Laplacian

Berardino Sciunzi·Giuseppe Spadaro·Domenico Vuono
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Abstract

We obtain optimal regularity results for solutions to vectorial $p$-Laplace equations $$ -{\boldsymbol \Delta}_p{\boldsymbol u}=-\operatorname{\bf div}(|D{\boldsymbol u}|^{p-2}D{\boldsymbol u}) = {\boldsymbol f}(x)\,\, \mbox{ in $\Omega$}\,.$$ More precisely we address the issue of global second order estimates for the stress field.

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Berardino Sciunzi, Giuseppe Spadaro, Domenico Vuono. 2025-02-24. Global second order optimal regularity for the vectorial $p$-Laplacian. https://arxiv.org/abs/2502.17067

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