We prove interior Hölder estimates for the spatial gradients of the viscosity solutions to the
singular or degenerate parabolic equation ut=|∇⁡ u| κ⁢ div⁡(|∇⁡ u| p-2⁢∇⁡ u), where …

We prove interior Hölder estimates for the spatial gradient of viscosity solutions to the
parabolic homogeneous p-Laplacian equation ut=|∇ u| 2− p div (|∇ u| p− 2∇ u), where 1< …

We introduce an evolution model à la Firey for a convex stone which tumbles on a beach
and undertakes an erosion process depending on some variational energy, such as …

The $ p $-Laplacian operator $\Delta_pu={\rm div}\left (|\nabla u|^{p-2}\nabla u\right) $ is not
uniformly elliptic for any $ p\in (1, 2)\cup (2,\infty) $ and degenerates even more when …

We introduce a new class of quasi-linear parabolic equations involving nonhomogeneous
degeneracy or/and singularity∂ tu=[| D u| q+ a (x, t)| D u| s] Δ u+(p-2) D 2 u Du| D u|, Du| D …

We consider the interior Hölder regularity of spatial gradient of viscosity solution to the
parabolic normalized p (x, t)-Laplace equation ut=(δ i j+(p (x, t)− 2) uiuj| D u| 2) uij with some …

In this paper, we investigate a weighted Dirichlet eigenvalue problem for a class of
degenerate operators related to the hh degree homogeneous pp-Laplacian {| D u| h− 1 Δ N …

We extend the symmetry result of Serrin\cite {S} and Weinberger\cite {W} from the Laplacian
operator to the highly degenerate game-theoretic $ p $-Laplacian operator and show that …

We consider the solution u of ut− Δ p G u= 0 in a (not necessarily bounded) domain Ω, such
that u= 0 in Ω at time t= 0 and u= 1 on the boundary of Ω at all times. Here, Δ p G is the game …

We consider the (viscosity) solution u ε of the elliptic equation ε 2 Δ p G u= u in a domain (not
necessarily bounded), satisfying u= 1 on its boundary. Here, Δ p G is the game-theoretic or …