Interior and boundary regularity results for strongly nonhomogeneous p,q-fractional problems

Jacques Giacomoni; Deepak Kumar; Konijeti Sreenadh

doi:10.1515/acv-2021-0040

Article

Interior and boundary regularity results for strongly nonhomogeneous p,q-fractional problems

Jacques Giacomoni , Deepak Kumar and Konijeti Sreenadh

Published/Copyright: September 25, 2021

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From the journal Advances in Calculus of Variations Volume 16 Issue 2

Abstract

In this article, we deal with the global regularity of weak solutions to a class of problems involving the fractional ( p , q ) -Laplacian, denoted by ( - Δ ) p s 1 + ( - Δ ) q s 2 for s 2 , s 1 ∈ ( 0 , 1 ) and 1 < p , q < ∞ . We establish completely new Hölder continuity results, up to the boundary, for the weak solutions to fractional ( p , q ) -problems involving singular as well as regular nonlinearities. Moreover, as applications to boundary estimates, we establish a new Hopf-type maximum principle and a strong comparison principle in both situations.

Keywords: nonhomogeneous nonlocal operator; singular nonlinearity; local and boundary Hölder continuity; maximum principle; strong comparison principle

MSC 2010: 35J60; 35R11; 35B45; 35D30

Communicated by Juha Kinnunen

Acknowledgements

The authors thank both anonymous referees for the careful reading of this paper and for their remarks and comments, which have improved the initial version of our work.

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Received: 2021-04-22

Accepted: 2021-08-09

Published Online: 2021-09-25

Published in Print: 2023-04-01

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Articles in the same Issue

https://doi.org/10.1515/acv-2021-0040

Keywords for this article

nonhomogeneous nonlocal operator; singular nonlinearity; local and boundary Hölder continuity; maximum principle; strong comparison principle