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arXiv · 2112.09087

Interior regularity results for inhomogeneous anisotropic quasilinear equations

Carlo Alberto Antonini·Giulio Ciraolo·Alberto Farina
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Abstract

We consider inhomogeneous $p$-Laplace type equations of the form $-\mathrm{div}\left(a(\nabla u)\right)=f$ in a possibly anisotropic setting. Under general assumptions on the source term $f$, we obtain quantitative Sobolev regularity results for the stress field $a(\nabla u)$ and weighted $L^2$ estimates for the Hessian of the solution. As far as we know, our results are new or refine the ones available in literature also when restricted to the Euclidean setting.

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Carlo Alberto Antonini, Giulio Ciraolo, Alberto Farina. 2021-12-16. Interior regularity results for inhomogeneous anisotropic quasilinear equations. https://arxiv.org/abs/2112.09087

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