JournalsaihpcVol. 29, No. 6pp. 833–859

Regularity for solutions of nonlocal, nonsymmetric equations

  • Héctor Chang Lara

    University of Texas at Austin, Department of Mathematics, 1 University Station C1200, Austin, TX 78712, United States
  • Gonzalo Dávila

    University of Texas at Austin, Department of Mathematics, 1 University Station C1200, Austin, TX 78712, United States
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Abstract

We study the regularity for solutions of fully nonlinear integro differential equations with respect to nonsymmetric kernels. More precisely, we assume that our operator is elliptic with respect to a family of integro differential linear operators where the symmetric parts of the kernels have a fixed homogeneity σ and the skew symmetric parts have strictly smaller homogeneity τ. We prove a weak ABP estimate and C1,αC^{1,\alpha } regularity. Our estimates remain uniform as we take σ2\sigma \rightarrow 2 and τ1\tau \rightarrow 1 so that this extends the regularity theory for elliptic differential equations with dependence on the gradient.

Cite this article

Héctor Chang Lara, Gonzalo Dávila, Regularity for solutions of nonlocal, nonsymmetric equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012), no. 6, pp. 833–859

DOI 10.1016/J.ANIHPC.2012.04.006