arXiv subjects

Shota Tateyama

Publications and source records attributed to Shota Tateyama.

3 recordsLinked to original sources

arXiv2020

On $L^p$-viscosity solutions of parabolic bilateral obstacle problems with unbounded ingredients

The global equi-continuity estimate on $L^p$-viscosity solutions of parabolic bilateral obstacle problems with unbounded ingredients is established when obstacles are merely continuous. The existence of $L^p$-viscosity solutions is established via an approximation of given data. The local Hölder continuity estimate on the space derivative of $L^p$-viscosity solutions is shown when the obstacles belong to $C^{1, β}$, and $p>n+2$.

math.AP↗

arXiv2019

On Lp-viscosity solutions of bilateral obstacle problems with unbounded ingredients

The global equi-continuity estimate on Lp-viscosity solutions of bilateral obstacle problems with unbounded ingredients is established when obstacles are merely continuous. The existence of Lp-viscosity solutions is established via an approximation of given data. The local Hölder continuity estimate on the first derivative of Lp-viscosity solutions is shown when the obstacles belong to C^{1,β}, and p>n.

math.AP↗

arXiv2019

Weak Harnack inequality for fully nonlinear uniformly parabolic equations with unbounded ingredients and applications

The weak Harnack inequality for $L^p$-viscosity supersolutions of fully nonlinear second-order uniformly parabolic partial differential equations with unbounded coefficients and inhomogeneous terms is proved. It is shown that Hölder continuity of $L^p$-viscosity solutions is derived from the weak Harnack inequality for $L^p$-viscosity supersolutions. The local maximum principle for $L^p$-viscosity subsolutions and the Harnack inequality for $L^p$-viscosity solutions are also obtained. Several further remarks are presented when equations have superlinear growth in the first space derivatives.

math.AP↗