In this paper, we study the Dirichlet problem of inhomogeneous infinity Laplace equation with strong absorptions: style='text-indent:20px;'> \begin{document}$ \begin{equation*} \begin{cases} \ \Delta_{\infty}u(x)-\lambda(x)(u(x))^{\gamma}_+ = f(x), &{\rm{in}}\ \Omega, \\ u(x) \phi(x), &{\rm{on}}\ \partial\Omega, \en...

In the present work, a nonlocal optimal design model has been considered as an approximation of corresponding classical or local problem. The new is driven by \begin{document}$ p $\end{document}-Laplacian equation, diffusion coefficient and cost functional belongs to broad class integrals. purpose this pa...

We describe the large-time asymptotics of solutions to heat equation for fractional Laplacian with added subcritical or even critical Hardy-type potential. The is governed by a self-similar solution equation, obtained as normalized limit at origin kernel corresponding Feynman-Kac semigroup.

Pushed by the rising interest in high resolution requirements and high-dimensional applications, the diffusion term in the Laplacian equation drives the condition number of the associated discretized operator to undesirable sizes for standard iterative methods to converge rapidly. In addition, for realistic values of the wavenumber k(x) in (1), the Helmholtz operator H becomes indefinite, destr...