Regularity and multiplicity results for fractional (p,q)-Laplacian equations

2019/02/01 by Goel, Divya, Kumar, Deepak, Sreenadh, K. · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.00395

Abstract

This article deals with the study of the following nonlinear doubly nonlocal equation: (-Δ)s1pu+\ba(-Δ)s2qu = \la a(x)|u|δ-2u+ b(x)|u|r-2 u, in \Om, u=0 on ℝn∖ \Om, where \Om is a bounded domain in ℝn with smooth boundary, 1< \de ≤ q≤ p p s1 and \la, \ba>0 are parameters. Here a∈ L(r)/(r-\de)(\Om) and b∈ L∞(\Om) are sign changing functions. We prove the L^∞ estimates, weak Harnack inequality and Interior Hölder regularity of the weak solutions of the above problem in the subcritical case (r

Cited by

• Kirchhoff-type equations involving the Fractional (p,q)-Laplacian

Related

• Multiplicity results of fractional p-Laplace equations with sign-changing and singular nonlinearity
• Interior and boundary regularity results for strongly nonhomogeneous p,q-fractional problems
• Fine Boundary Regularity For The Fractional (p,q)-Laplacian
• Global Hölder regularity for the fractional p-Laplacian
• Local behaviour and existence of solutions of the fractional (p,q)-Laplacian