In this article, well-posedness of stochastic anisotropic $p$-Laplace equation driven by L\'evy noise is shown. Such an in deterministic setting was considered Lions [7]. The results obtained article can be applied to solve a large class semilinear and quasilinear partial differential equations.

This paper concerns an optimization problem related to the Poisson equation for the p-Laplace operator, subject to homogeneous Dirichlet boundary conditions. Physically the Poisson equation models, for example, the deformation of a nonlinear elastic membrane which is fixed along the boundary, under load. A particular situation where the load is represented by a characteristic function is invest...

Abstract In this paper, we study the second-order Sobolev regularity of solutions to parabolic p -Laplace equation. For any -parabolic function u , show that $$D(\left| Du\right| ^{\frac{p-2+s}{2}}Du)$$ D ( u p</mml:m...

In order to overcome the difficulties of low computational efficiency and high memory requirement in the conventional boundary element method for solving large-scale potential problems, a fast multipole boundary element method for the problems of Laplace equation is presented. through the multipole expansion and local expansion for the basic solution of the kernel function of the Laplace equati...

Effects of the uniform transverse magnetic field on the transient free convective flows of a nanofluid with generalized thermal transport between two vertical parallel plates have been analyzed. The fluid temperature is described by a time-fractional differential equation with Caputo derivatives. Closed form of the temperature field is obtained by using the Laplace transform and fractional deri...

The main idea behind the Laplace transformation is that we can solve an equation (or system of equations) containing differential and integral terms by transforming the equation in time (t) domain into Laplace (2) domain. For example, we can use Laplace transforms to turn an initial value problem into an algebraic problem which is easier to solve. After we solved the problem in Laplace domain w...