Related papers: A finite difference method for the variational $p$…

In this paper we study solutions, possibly unbounded and sign-changing, of the following problem: -\D_{\lambda} u=|x|_{\lambda}^a |u|^{p-1}u, in R^n,\;n\geq 1,\; p>1, and a \geq 0, where \D_{\lambda} is a strongly degenerate elliptic…

In this paper we study numerical approximations of the evolution problem for the nonlocal $p$-Laplacian with homogeneous Neumann boundary conditions. First, we derive a bound on the distance between two continuous-in-time trajectories…

In this paper we construct two algorithms to approximate the minimizer of a discrete functional which comes from using a discontinuous Galerkin method for a variational problem related to the $p(x)$-Laplacian. We also make some numerical…

The Dominative $p$-Laplacian is the operator defined for $2\le p < \infty$ as follows: \begin{equation}\label{dominativep} \mathcal{L}_{p}u(x)=\frac{1}{p}\left(\lambda_{1}+\ldots+\lambda_{N-1}\right)+\frac{(p-1)}{p}\lambda_{N},…

This work tackles an inverse boundary value problem for a $p$-Laplace type partial differential equation parametrized by a smoothening parameter $\tau \geq 0$. The aim is to numerically test reconstructing a conductivity type coefficient in…

We study solution techniques for parabolic equations with fractional diffusion and Caputo fractional time derivative, the latter being discretized and analyzed in a general Hilbert space setting. The spatial fractional diffusion is realized…

In the past decades, the finite difference methods for space fractional operators develop rapidly; to the best of our knowledge, all the existing finite difference schemes, including the first and high order ones, just work on uniform…

In the process of constructing invariant difference schemes which approximate partial differential equations we write down a procedure for discretizing an arbitrary partial differential equation on an arbitrary lattice. An open problem is…

We consider a degenerate parabolic equation associated with the fractional $% p $-Laplace operator $\left( -\Delta \right) _{p}^{s}$\ ($p\geq 2$, $s\in \left( 0,1\right) $) and a monotone perturbation growing like $\left\vert s\right\vert…

This paper mainly investigates the analytic solutions for the approximation of $p$-Laplacian problem. Through an approximation mechanism, we convert the nonlinear partial differential equation with Dirichlet boundary into a sequence of…

We prove the existence of a weak solution to the problem \begin{equation*} \begin{split} -\Delta_{p}u+V(x)|u|^{p-2}u & =f(u,|\nabla u|^{p-2}\nabla u), \ \ \ \\ u(x) & >0\ \ \forall x\in\mathbb{R}^{N}, \end{split} \end{equation*} where…

We set up a general framework tailor-made to solve complement value problems governed by symmetric nonlinear integrodifferential $p$-L\'evy operators. A prototypical example of integrodifferential $p$-L\'evy operators is the well-known…

The aim of this paper is to prove multiplicity of solutions for nonlocal fractional equations modeled by $$ \left\{ \begin{array}{ll} (-\Delta)^s u-\lambda u=f(x,u) & {\mbox{ in }} \Omega\\ u=0 & {\mbox{ in }} \mathbb{R}^n\setminus…

In this paper, we consider a nonlinear beam equation with the p-biharmonic operator, where $1 < p < \infty$. Using a change of variable, we transform the problem into a system of differential equations and prove the existence, uniqueness…

We consider the critical $p$-Laplacian system \begin{equation}\label{92} \begin{cases}-\Delta_p u-\frac{\lambda a}{p}|u|^{a-2}u|v|^b =\mu_1|u|^{p^\ast-2}u+\frac{\alpha\gamma}{p^\ast}|u|^{\alpha-2}u|v|^{\beta}, &x\in\Omega,\\ -\Delta_p…

In this paper, we assume that $q>0$, $p>1$ and $s\in(0,1)$ , and consider the following nonlinear fractional p-Laplacian equations on finite graphs: \begin{equation*} \left\{ \begin{array}{lll} \partial_t u^q(x,t)+(-\Delta)_p^su=0,\\[15pt]…

We introduce and analyze a numerical approximation of the porous medium equation with fractional potential pressure introduced by Caffarelli and V\'azquez: \[ \partial_t u = \nabla \cdot (u^{m-1}\nabla (-\Delta)^{-\sigma}u) \qquad…

We analyze an adaptive finite element/boundary element procedure for scalar elastoplastic interface problems involving friction, where a nonlinear uniformly monotone operator such as the p-Laplacian is coupled to the linear Laplace equation…

For finite difference discretizations with linear complexity and provably convergent to weak solutions of the second boundary value problem for the Monge-Amp\`ere equation, we give the first proof of uniqueness. The boundary condition is…

We introduce a new numerical method, based on Bernoulli polynomials, for solving multiterm variable-order fractional differential equations. The variable-order fractional derivative was considered in the Caputo sense, while the…