$$C^{\sigma +\alpha }$$Cσ+α regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels

  title={\$\$C^\{\sigma +\alpha \}\$\$C$\sigma$+$\alpha$ regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels},
  author={Joaquim Serra},
  journal={Calculus of Variations and Partial Differential Equations},
  • J. Serra
  • Published 5 May 2014
  • Mathematics
  • Calculus of Variations and Partial Differential Equations
We establish $$C^{\sigma +\alpha }$$Cσ+α interior estimates for concave nonlocal fully nonlinear equations of order $$\sigma \in (0,2)$$σ∈(0,2) with rough kernels. Namely, we prove that if $$u\in C^{\alpha }(\mathbb {R}^n)$$u∈Cα(Rn) solves in $$B_1$$B1 a concave translation invariant equation with kernels in $$\mathcal L_0(\sigma )$$L0(σ), then u belongs to $$C^{\sigma +\alpha }(\overline{B_{1/2}})$$Cσ+α(B1/2¯), with an estimate. More generally, our results allow the equation to depend on x in… 

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