Preprint

Inserted: 8 jul 2026
Last Updated: 8 jul 2026

Pages: 41
Year: 2026

Abstract:

We prove global higher integrability of the gradient for solutions to nonlinear PDEs with homogeneous Dirichlet condition. We work with general open sets (i.e. not necessarily bounded), under a minimal thickness assumption of the complement. The main focus is on improving the global summability of the gradient, by preserving the "zero trace" Sobolev class. We pay due attention to providing precise a priori estimates. As an application, we get universal global Hölder estimates for solutions of the super-homogeneous Lane-Emden equation for the $N-$Laplacian, in contractible open sets with finite inradius.

Keywords: $p$-Laplacian, Poincare inequality, boundary regularity, thickness

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• brabra_global_final_sup.pdf