Regularity of solutions for degenerate or singular fully nonlinear integro-differential equations

2024/08/27 by Wang, Jiangwen, Jiang, Feida · 4 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.14779

Abstract

We study a series of regularity results for solutions to a degenerate or singular fully nonlinear integro-differential equation of the form - ( σ₁(|Du|) + a(x) σ₂(|Du|) ) I_τ(u,x) = f(x). In the degenerate case, we establish borderline regularity, provided the inverse of the degeneracy law σ₂ is Dini-continuous. In addition, we show Schauder-type higher regularity at local extremum points for a specific non-local degenerate equation. In the singular case, we establish Hölder continuity of the gradient for solutions to a general non-local equation. It is noteworthy that these results are new even in the case a(x) ≡ 0 . Finally, as a byproduct of the borderline regularity analysis, we demonstrate how our methods can be applied to study of the corresponding regularity for a class of degenerate non-local normalized p-Laplacian equations.

Cited by

• Regularity for fully nonlinear degenerate parabolic equations with strong absorption
• Existence and nonexistence of viscosity solutions for a class of degenerate/singular eigenvalue type equations
• Regularity theory for degenerate fully nonlinear nonlocal equations with a Hamiltonian term
• Regularity for the normalized p-Laplacian equation with an arbitrary degeneracy law

Related

• Regularity estimates for fully nonlinear integro-differential equations with nonhomogeneous degeneracy
• Regularity for a class of degenerate fully nonlinear nonlocal elliptic equations
• Regularity for solutions of non local, non symmetric equations
• Interior regularity estimates for fully nonlinear equations with arbitrary nonhomogeneous degeneracy laws
• Global regularity results for a class of singular/degenerate fully nonlinear elliptic equations