For differential games of fixed duration of linear dynamical systems with nonquadratic payoff functionals, it is proved that the value and the optimal strategies as saddle point exist whenever the associated pseudo-Riccati equation has a regular solution P(t,x). Then the closed-loop optimal strategies are given by u(t) = −R−1B∗P(t,x(t)), v(t) = −S−1C∗P(t,x(t)). For differential game problems of...

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...