Abstract We propose a new finite difference scheme for the degenerate parabolic equation $$\begin{aligned} \partial _t u - \text{ div }(|\nabla u|^{p-2}\nabla u) =f, \quad p\ge 2. \end{aligned}$$ ? t u - ...

We prove C regularity for a thin obstacle problem for the p-laplace equation. Due to the nonlinearity of the p-laplace operator we can not use the same methods used for the Laplace case, instead we use techniques developed by E. de Giorgi. AMS Classification: 35R35, 35J60, 35B65.

this article is devoted to study of the autoconvolution equations and generalized mittag-leffler functions. these types of equations are given in terms of the laplace transform convolution of a function with itself. we state new classes of the autoconvolution equations of the first kind and show that the generalized mittag-leffler functions are solutions of these types of equations. in view of ...

In this article, we study the following anisotropic p-Laplacian equation with variable exponent given by \begin{equation*} (P) \begin{cases} -\Delta_{H,p}u =\frac{\lambda f(x)}{u^{q(x)}}+g(u) \ \text{ in }\Omega,\\ u > 0 }\Omega,\ u=0\text{ on }\partial\Omega, \end{cases} \end{equation*} under assumption $\Omega$ is a bounded smooth domain $\mathbb{R}^N$ $p,N\geq 2$, $\lambda>0$ and $0 < q \in ...