JournalsaihpcVol. 36, No. 7pp. 1869–1902

Regularity theory for Ln-viscosity solutions to fully nonlinear elliptic equations with asymptotical approximate convexity

  • Qingbo Huang

    Department of Mathematics & Statistics, Wright State University, Dayton, OH 45435, United States of America
Regularity theory for Ln-viscosity solutions to fully nonlinear elliptic equations with asymptotical approximate convexity cover
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Abstract

We develop interior W2,p,μW^{2,p,\mu } and W2,BMOW^{2,\text{BMO}} regularity theories for LnL^{n}-viscosity solutions to fully nonlinear elliptic equations T(D2u,x)=f(x)T(D^{2}u,\:x) = f(x), where T is approximately convex at infinity. Particularly, W2,BMOW^{2,\text{BMO}} regularity theory holds if operator T is locally semiconvex near infinity and all eigenvalues of D2T(M)D^{2}T(M) are at least CM(1+σ0)−C\|M\|^{−(1 + \sigma _{0})} as MM\rightarrow \infty . W2,BMOW^{2,\text{BMO}} regularity for some Isaacs equations is given. We also show that the set of fully nonlinear operators of W2,BMOW^{2,\text{BMO}} regularity theory is dense in the space of fully nonlinear uniformly elliptic operators.

Cite this article

Qingbo Huang, Regularity theory for Ln-viscosity solutions to fully nonlinear elliptic equations with asymptotical approximate convexity. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 7, pp. 1869–1902

DOI 10.1016/J.ANIHPC.2019.06.001