C1,α regularity for the normalized p-Poisson problem
Attouchi, A., Parviainen, M., & Ruosteenoja, E. (2017). C1,α regularity for the normalized p-Poisson problem. Journal de Mathématiques Pures et Appliquées, 108(4), 553-591. https://doi.org/10.1016/j.matpur.2017.05.003
Published inJournal de Mathématiques Pures et Appliquées
© 2017 Elsevier Masson SAS. This is a final draft version of an article whose final and definitive form has been published by Elsevier. Published in this repository with the kind permission of the publisher.
We consider the normalized p -Poisson problem − Δ N p u = f in Ω ⊂ R n . The normalized p -Laplacian Δ N p u := | Du | 2 − p Δ p u is in non-divergence form and arises for example from stochastic games. We prove C 1 ,α loc regularity with nearly optimal α for viscosity solutions of this problem. In the case f ∈ L ∞ ∩ C and p> 1 we use methods both from viscosity and weak theory, whereas in the case f ∈ L q ∩ C , q> max( n, p 2 , 2), and p> 2 we rely on the tools of nonlinear potential theory
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Related funder(s)Academy of Finland
Funding program(s)Research post as Academy Research Fellow, AoF
Additional information about fundingMP is supported by the Academy of Finland (No. 260791) and ER is supported by the Vilho, Kalle and Yrjö Väisälä foundation.
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