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

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 $(-\Delta {)}_p^{s_1}+(-\Delta {)}_q^{s_2}$, for $s_2,s_1\in (0,1)$ and $1<p,q<\infty$. 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 new Hopf type maximum principle and strong comparison principle in both situations.

arXiv comment43 pages

References in corpus (4)

• Nonlocal diffusion and applications
• Local behavior of fractional $p$-minimizers
• A Hopf's lemma and a strong minimum principle for the fractional $p$-Laplacian
• Multiplicity results for $(p,q)$ fractional elliptic equations involving critical nonlinearities

Cited by in corpus (2)

• Regularity for nonlocal problems with non-standard growth
• Global regularity results for non-homogeneous growth fractional problems