$$C^{\sigma +\alpha }$$ C σ + α regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels
2015; Springer Science+Business Media; Volume: 54; Issue: 4 Linguagem: Inglês
10.1007/s00526-015-0914-2
ISSN1432-0835
Autores Tópico(s)Advanced Harmonic Analysis Research
ResumoWe establish $$C^{\sigma +\alpha }$$ interior estimates for concave nonlocal fully nonlinear equations of order $$\sigma \in (0,2)$$ with rough kernels. Namely, we prove that if $$u\in C^{\alpha }(\mathbb {R}^n)$$ solves in $$B_1$$ a concave translation invariant equation with kernels in $$\mathcal L_0(\sigma )$$ , then u belongs to $$C^{\sigma +\alpha }(\overline{B_{1/2}})$$ , with an estimate. More generally, our results allow the equation to depend on x in a $$C^\alpha $$ fashion. Our method of proof combines a Liouville theorem and a blow-up (compactness) procedure. Due to its flexibility, the same method can be useful in different regularity proofs for nonlocal equations.
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