Interior regularity results for inhomogeneous anisotropic quasilinear equations

Carlo Alberto Antonini; Giulio Ciraolo; Alberto Farina

Interior regularity results for inhomogeneous anisotropic quasilinear equations

Analysis of PDEs 2021-12-17 v1

Authors: Carlo Alberto Antonini , Giulio Ciraolo , Alberto Farina

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.

Keywords

p-Laplace equation interior regularity anisotropic Sobolev regularity stress field

Cite

@article{arxiv.2112.09087,
  title  = {Interior regularity results for inhomogeneous anisotropic quasilinear equations},
  author = {Carlo Alberto Antonini and Giulio Ciraolo and Alberto Farina},
  journal= {arXiv preprint arXiv:2112.09087},
  year   = {2021}
}

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