The relationship between solutions of the sinh-Laplace equation and the determination of various kinds of surfaces of constant Gaussian curvature, both positive and negative, will be investigated here. It is shown that when the metric is given in a particular set of coordinates, the Gaussian curvature is related to the sinh-Laplace equation in a direct way. The fundamental equations of surface ...

Abstract. Cell-centered and vertex-centered finite volume schemes for the Laplace equation with homogeneous Dirichlet boundary conditions are considered on triangular meshes and their Voronoi duals. On a two-dimensional convex polygonal domain, it is shown that a suitable combination of the solutions of these two schemes converges with second-order accuracy towards the exact solution in the L n...

We prove an elliptic Harnack's inequality for a general form of parabolic equation that generalizes both the standard p $p$ -Laplace and normalized version has been proposed in stochastic game theory. This does not require intrinsic waiting time we get estimate with same level on sides inequality.

We consider an inverse problem of recovering the non-linearity in one dimensional variable exponent $p(x)$-Laplace equation from Dirichlet-to-Neumann map. The can be recovered up to natural obstruction rearrangements. main technique is using a Muntz-Szasz theorem after reducing determining function its $L^p$-norms.

In 1983, a preconditioner was proposed [J. Comput. Phys. 49 (1983) 443] based on the Laplace operator for solving the discrete Helmholtz equation efficiently with CGNR. The preconditioner is especially effective for low wavenumber cases where the linear system is slightly indefinite. Laird [Preconditioned iterative solution of the 2D Helmholtz equation, First Year’s Report, St. Hugh’s College, ...

We study the entire solutions of the p-Laplace equation − div(|∇u|p−2∇u) + a(x, y)W ′(u(x, y)) = 0, (x, y) ∈ R where a(x, y) is a periodic in x and y, positive function. Here W : R → R is a two well potential. Via variational methods, we show that there is layered solution which is heteroclinic in x and periodic in y direction.

The present paper deals with a nonlocal problem under homogeneous Dirichlet boundary conditions, set in a bounded smooth domain Ω of R . The problem studied is a stationary version of the original Kirchhoff equation involving the p-Laplace operator. The question of the existence of weak solutions is treated. Using variational approach and applying the Mountain Pass Theorem together with Fountai...

although elzaki transform is stronger than sumudu and laplace transforms to solve the ordinary differential equations withnon-constant coefficients, but this method does not lead to finding the answer of some differential equations. in this paper, a method is introduced to find that a differential equation by elzaki transform can be ‎solved?‎

The kinetics of a diffusing particle near a reversible trap may be described by an extension of the Feynman-Kac equation to the case of reversible binding, which can occur within a finite reaction sphere. We obtain the Green's function solution for the Laplace transform of this equation when the particle is initially either bound or unbound. We study the solution in the time-domain by either in...