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arXiv · 2607.07238

Regularity for eigenvalue-type equations in sets with thick complement

Lorenzo Braglia·Lorenzo Brasco
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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.

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Lorenzo Braglia, Lorenzo Brasco. 2026-07-08. Regularity for eigenvalue-type equations in sets with thick complement. https://arxiv.org/abs/2607.07238

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