논문
Parabolic Harnack inequality of viscosity solutions on Riemannian manifolds
- 저자Soojung Kim, Lee. K. A.
- 학술지Journal of functional analysis 267(7), 2152-2198
- 등재유형
- 게재일자(2014)
We consider viscosity solutions to nonlinear uniformly parabolic equations in nondivergence form on a Riemannian manifold $M$ with the sectional curvature bounded from below by $−κ$ for $κ≥0.$ In the elliptic case, Wang and Zhang [24] recently extended the results of [5] to nonlinear elliptic equations in nondivergence form on such $M$, where they obtained the Harnack inequality for classical solutions. We establish the Harnack inequality for nonnegative viscosity solutions to nonlinear uniformly parabolic equations in nondivergence form on $M$. The Harnack inequality of nonnegative viscosity solutions to the elliptic equations is also proved.
We consider viscosity solutions to nonlinear uniformly parabolic equations in nondivergence form on a Riemannian manifold $M$ with the sectional curvature bounded from below by $−κ$ for $κ≥0.$ In the elliptic case, Wang and Zhang [24] recently extended the results of [5] to nonlinear elliptic equations in nondivergence form on such $M$, where they obtained the Harnack inequality for classical solutions. We establish the Harnack inequality for nonnegative viscosity solutions to nonlinear uniformly parabolic equations in nondivergence form on $M$. The Harnack inequality of nonnegative viscosity solutions to the elliptic equations is also proved.
